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Hanno Rund

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Publications: Books

  • 1959 “The Differential Geometry of Finsler Spaces” Springer-Verlag (Berlin-Göttingen-Heidelberg), Grundlehren Serie, 289 pp.

  • 1966 “The Hamilton-Jacobi Theory in the Calculus of Variations” D. Van Nostrand (London u. New York), 404 pp.

  • 1970 “Introduction to Algebra and Analysis” (with J.H.V.D. Merwe et al) McGraw Hill (New York-Johannesburg), 450 pp.

  • 1973 “The Hamilton-Jacobi Theory in the Calculus of Variations”, revised and augmented reprint, R.E. Krieger Publishing Co., (New York), XV–440 pp.

  • 1975 “Tensors, Differential Forms, and Varational Principles” (with D. Lovelock), Wiley Interscience, pp.364.

  • 1982 “The Differential Geometry of Finsler Spaces”, Russian Translation by G.S. Asanov (Nauka, Moscow, USSR)(Expanded and Modernized Version of 1959 Edition, three additional chapters by author, two addenda by Asanov).

  • 1990 “Tensors, Differential Forms, and Variational Principles” (with D. Lovelock), Dover Publications (N.Y.) Reprint of 1975 Edition, with new Appendix on global geometry by H.R.).

Monographs

  • 1971 “Invariant theory of variational problems on subspaces of a Riemannian Manifold” Hamburg. Math. Einzelschriften, N.5., Göttingen (55 pages).

  • 1981 “Generalized Gauge Fields and Fibre Bundles” Studia-Series Mathematica (125 pages)

Professional Journal Articles Published since 1950

  • 1950 Finsler spaces considered as locally Minkowskian spaces. Ph.D.-thesis, University of Cape Town, 107 pp.

  • 1951 Über die Parallelverschiebung in Finslerschen Räumen. Math.Z. 54, 115–128.

  • 1952 A theory of curvature in Finsler spaces. Colloque de Topologie de Strasbourg (1951), no.IV, 12 pp. La Bibliothèque Nationale et Universitaire.

  • 1952 Zur Begründung der Differentialgeometrie in Minkowskischen Räumen. Arch.Math. 3, 60–69.

  • 1952 Über die Hamiltonsche Funktion bei allgemeinen dynamischen Systemen. Arch.Math. 3, 207–215.

  • 1952 Eine Krümmungstheorie in Finslerschen Räumen. Math.Ann. 125, 1–18.

  • 1952 Über Kurven and Flächen in metrischen Räumen endlicher Dimensionszahl. Habilitationsschrift, Univ. of Freiburg, 70 pp.

  • 1952 The theory of subspaces of a Finsler space. Part I. Math.Z. 56, 363–375.

  • 1953 The theory of subspaces of a Finsler space. Part. II. Math.Z.57, 193–210.

  • 1953 The scalar form of Jacobi’s equation in the calculus of variations. Ann.Mat.pura appl. (IV)35, 183–202.

  • 1953 On the geometry of generalized metric spaces. Convegno Internazionale di Geometria Differenziale, Bologna, 113–131.

  • 1953 Applications des méthodes de la géometrie métrique generalisée à la dynamique théorique. Géometrie differentielle, Colloques Internationaux de C.W.R.S.,Paris, 41–51.

  • 1953 On the analytical properties of curvature tensors in Finsler spaces. Math.Ann.127, 82–104.

  • 1954 Über nicht-holonome allgemeine metrische Geometric Math.Nachr.11,61–80.

  • 1956 Hypersurfaces of a Finsler space. Canadian J.Math.8, 487–503.

  • 1957 Über allgemeine nicht-holonome und dissipative dynamische Systeme. Bericht von der Riemann-Tagung, Deutsche Akademie der Wissenschaften, Berlin, 269–279.

  • 1958 The theory of non-linear connections. Koninkl. Nederl. Akad. Wetensch. Amsterdam, Proc/S.61. 335–347.

  • 1959 Some remarks concerning Caratheodory’s method of equivalent integrals in the calculus of variations. Koninkl. Nederl.Akad.Wetensch.Amsterdam, Proc. A.62, 135–141.

  • 1959 The Differential Geometry of Finsler Spaces. Springer-Verlag, Berlin-Heidelberg-Göttingen, Die Grundlehren der mathematischen Wissenschaften. XV-284 pp.

  • 1961 Dynamics of particles with internal spin. Ann. Physik (7)7, 17–27.

  • 1961 The theory of problems in the calculus of variations whose Lagrangians involve higher order derivatives: a new approach. Ann.Mat.pura appl.(IV)55, 77–104.

  • 1961 Some curvature properties of solution manifolds of variational problems involving multiple integrals. Tydskr.Natuurw. 1,171–178.

  • 1962 The Lagrangian formalism in relativistic dynamics. Nuovo Cimento (X) 23,227–232.

  • 1962 Über Finslersche Räume mit speziellen Krümmungseigenschaften. Monatsh. Math. 66, 241–251.

  • 1962 The world view of modern theoretical physics. Comm.Univ. of South Africa A 13, 1–12.

  • 1962 A characteristic property of Finsler spaces of constant curvature. Tydskr. Natuurw. 2, 63–70.

  • 1962 General relativistic wave equations. Tydskr. Natuurw. 2, 157–165.

  • 1963 Curvature properties of hypersurfaces of Finsler and Minkowskian spaces. Tensor (N.S.)14, 226–244.

  • 1963 On the Weierstrass excess functions of multiple parameter-invariant integrals in the calculus of variations. Tydskr.Natuurw., 3, 168–179.

  • 1963 A general theory of multiple integral problems in the calculus of variations. 1963 Colloquium on the calculus of variations, University of South Africa, 88–114.

  • 1964 On a certain operator-differential equation. Tydskr.Naturuw. 4, 27–30.

  • 1964 Canonical formalism for parameter-invariant integrals in the calculus of variations whose Lagrange functions involve second order derivatives. Ann.Mat.pura appl. 64, 99–108.

  • 1964 Problems in the calculus of variations whose unknown functions are tensor components.

  • 1964 Colloquium on the calculus of variations, University of South Africa, 129–174.

  • 1965 The intrinsic and induced curvature theories of subspaces of a Finsler space. Tensor (N.S.)16, 294–312.

  • 1965 Calculus of variations on complex manifolds. 1965 Colloquium on the calculus of variations. University of South Africa, 10–85.

  • 1966 Variational problems involving combined tensor fields. Abhandlungen Math.Sem. Univ. Hamburg 29, 243–262.

  • 1966 The Hamilton-Jacobi theory in the calculus of variations. D. van Nostrand Co., Ltd., London and New York, XIV + 404 pp.

  • 1966 A Hamiltonian formalism in relativistic mechanics. Chapter 34: “Perspectives in geometry and relativity”. University of Indiana Press, Bloomington, Ind., U.S.A., 325–339.

  • 1966 Über die physikalische Bedeutung des Laplace-Lenz Vektors. Acta phys.Austriaca, 24, 365–367.

  • 1966 Finsler spaces in geodesic correspondence. Tydskr. Natuurw.6, 243–254.

  • 1967 Generalized metrics on complex manifolds. Mathematische Nachrichten,33,55–77.

  • 1967 Invariance properties of variational principles: their general implications in physical field theories. Tydskr.Natuurw.,7, 474–497.

  • 1967 Invariant variational problems for geometric objects, Tensor (N.S.)18, 239–258.

  • 1967 On a class of variational principles associated with boundary value problems. Joint Math.Coll.1967: University of South Africa and University of the Witwatersrand, 1–29.

  • 1967 Theory of generalized connections and curvature on complex manifolds. Joint Math. Coll.

  • 1967:University of South Africa and University of the Witwatersrand,47–99.

  • 1968 Systems of linear equations as canonical or Euler-Lagrange equations. J.Math.Phys. 8, 2059–2062.

  • 1968 A geometric theory of multiple integral problems in the calculus of variations. Canadian J.Math.20, 639–659.

  • 1968 A canonical formalism for multiple integral problems in the calculus of variations. Aequationes Math.3, 44–63. [also Notices Amer.math.Soc.393].

  • 1969 Structural invariance of Hamiltonian systems. Tydskr. Natuurw.9, 181–190.

  • 1969 Parameter-dependent canonical transformations. Tensor (N.S.)20, 213–228.

  • 1669 Multiple integral isoperimetric problems as problems of Lagrange in the calculus of variations. Joint Math.Coll.1968/69:University of South Africa and the University of the Witwatersrand, 320–355.

  • 1970 The reduction of certain boundary value problems by means of transversality conditions. Numerische Mathematik.15, 49–56.

  • 1970 (With J. H.V.C. Merwe et al.) Introduction to modern algebra and analysis, McGraw-Hill (New York and Johannesburg), 452 pp.

  • 1970 Canonical theory of higher order multiple integral problems in the calculus of variations. Tydskr.Natuurw.10, No.3, 15 pp.

  • 1970 Curvature invariants associated with complete sets of fundamental forms of hyper-surfaces of Riemannian manifolds. Tensor (N.S.)22, approx.20 pp.

  • 1970 (With J.H. Beare) Variational problems involving direction dependent fields. Monograph M2, University of South Africa Mathematical MonographSeries (1970), approx.80 pp.

  • 1970 Integral formulae on hypersurfaces in Riemannian manifolds. Annali di Mat.(1971), approx.25 pp.

  • 1974 “Transversality and Fields of Extremals of Multiple Integral Problems in the Calculus of Varations”, Aequationes Math.10, 236–261.

  • 1974 “Transformation Theory of the Canonical Formalism Associated with Multiple Integral Varational Problems”, Tensor (N.S.)28, 205–217.

  • 1974 “Systems of Non-linear Partial Differential Equations for Coherent Optical Pulse Propagation in an Inhomogeneously Broadened Medium and Associated Conservation Laws”, Optics Communications, 12, 123–128.

  • 1974 “Sufficiency Conditions for Multiple Integral Control Problems”, J.Opt.Theory Appl.13, 125–138.

  • 1974 “An Integral Invariant Associated with the Geodesic Field Theory of Weyl in the Calculus of Varations of Multiple Integrals”, Utilitas Math.5, 93–112.

  • 1974 “Integral Formulae Associated with the Euler-Lagrange Operators of Multiple Integral Problems in the Calculus of Variations”, Aequationes Math.11, 38–55.

  • 1975 “The Hamilton-Jacobi Theory of the Geodesic Fields of Caratheodory in the Calculus of Variations of Multiple Integrals”, Proceedings of the International Caratheodory Centenary symposium, Athens (1973), Greek Mathematical Society, pp.496–536.

  • 1975 “The Equation of Geodesic Deviation of Levi-Civita — Its Generalizations and Implications”, “Proceedings of the International Centenary Celebration in Honor of Levi-Civita, Academia Nazionale Dei Lincei”, Rome 1973, pp.77–112.

  • 1975 “A Divergence Theorem for Finsler Metrics and a Gauss-Bonnet Type Formula”, Monatshefte für Mathematik, 79, pp.233–252.

  • 1975 “Conservations Criteria, Canonical Transformations, and Integral Invariants in the Field Theory of Caratheodory for Variational Problems”, Aquationes Math., 13, pp.121–149.

  • 1975 (with H.J.Oosthuizen), “A Canonical Theory of the Classical Electromagnetic Field” Utilitas Math., 7, pp.295–230.

  • 1975 “Applications of Backlund Transformations to the Theory of Surfaces”, Boll. Unione Mat.Italiana,12, pp.297–313.

  • 1976 “Variational Problems and Backlund Transformations Associated with the Sine-Gordon and Korteweg-de Vries Equations and their Generalizations”, Proc. Nashville Conference on Contact Transformations, Springer Lecture Notes, in Mathematiacs, Vol.515, pp.199–266.

  • 1976 “Pontryagin Functions for Multiple Integral Problems”, J.Opt.Theory Appl., 18, pp. 511–520.

  • 1976 “Clebsch Representations on Manifolds”, In “Topics in Differential Geometry”, Academic Press, pp.111–133.

  • 1976 “Backlund Transformations Associated with 4-Dimensional Generalized Wave Equations”, Abh.Math.Sem.Univ.Hamburg, 45,pp.207–217.

  • 1976 “Adjoint problems in the Calculus of Variations of Multiple Integrals”, Quaestiones Math.,1,pp.29–82.

  • 1977 “Reciprocal Relations for Fluid Flows Generated by Divergence-Free Geometric Object Fields”, Tensor (N.S.),31, pp.55–63.

  • 1977 “Clebsch Potentials in the Theory of Electromagnetic Fields Admitting Electric and Magnetic Charge Distributions”, J.Math.Phys.,18, pp.84–95.

  • 1977 “Energy-Momentum Tensors in the Theory of Electromagnetic Fields Admitting Electric and Magnetic Charge Distributions”, J.Math.Phys.18, 1312–1315.

  • 1977 “The Formulation of Variational Principles by Means of Clebsch Potentials”, in “The Significance of Nonlinearity in the Natural Sciences”, Studies in Natural Sciences, Vol. 13 (Plenum Press, New York), 121–144.

  • 1977 “Clebsch Potentials and Variational Principles in the Theory of Dynamical Systems”, Arch.Rat.Mech.Analysis 65, 305–344.

  • 1978 “Clebsch Representations in the Theory of Minimum Energy Equilibrium Solution in Magnetohydrodynamics”, Journal of Plasma Physics, 20, 329–344 (with D.R. Wells).

  • 1978 Systems of Total Differential Equations and the Group SL(N,R), Tensor (N.S.)32, 373–379.

  • 1978 “Evolution Equations and Curvature Forms. Part I — Equations of the Sine-Gordon Type”, Utilitas Mathematica 14, pp.189–218.

  • 1979 Variational Derivation and Uniqueness of the Equation of Motion of a Particle in a Classical Gauge Field, Hardronic Journal Vol.2, pp.67–90.

  • 1979 Representation of the Duals of Gauge Field Tensors, Journal of Mathematical Physics.20, pp.1392–1397.

  • 1979 Generalized Gauge Field Theories. Vol.1, C.R./Math.Rep.Acad.Sci.Canada pp.83–86.

  • 1979 Decompositions of Connection and Curvature Forms. Tensor (N.S.)33, pp.97–108.

  • 1979 Evolution Equations and Curvature Forms. Part II–Equations of the Korteweg-de Vries type. Utilitas Mathematica. 15, 217–243.

  • 1979 Clebsch Representations and Relativistic Dynamical Systems. Arch.Rat.Mech. Analysis 71, 199–220.

  • 1980 Direction-Dependent Connection and Curvature Forms. Abh.Math.Sem.Univ. Hamburg 50, 186–207.

  • 1980 Connection and Curvature Forms Generated by Invariant Variational Principles. Resultate Math.3, 74–120.

  • 1981 Connections in Generalized Gauge Fields, In Christoffel Centenary Volume, 550–560, Birkhäuser Verlag, Basel.

  • 1981 An Extension of Noether’s Theorem to Transformations Involving Position-Dependent Parameters and their Derivatives. Foundations of Physics, 11, 809–838.

  • 1981 Subspaces of Manifolds with Direction-Dependent Connections. Tensor (N.S.), 35, 139–154.

  • 1981 Eu1er-Lagrange Equations as Divergence Conditions. Quaest.Math.4, 229–253.

  • 1982 Invariance theory of distributions associated with multiple integral problems in the calculus of variations. Tensor (N.S.)39, 45–66.

  • 1982 The construction of the complete figure in the calculus of variations of multiple integrals: a direct approach. Quaest.Math.5, 187–218.

  • 1982 Differential-geometric and variational background of classical gauge field theories. Aequations Math.24, 121–174.

  • 1983 Invariance identities associated with finite gauge transformations and the uniqueness of the equations of motion of a particle in a classical gauge field. Foundations of Physics 13, 93–114.

  • 1983 Classes of connections associated with distributions on product spaces. Quaest. Math.6, 363–384.

  • 1983 Lectures on Symplectic Geometry and Geometric Quantization. Colloquium Publications of the University of South Africa, 89 pp.

  • 1983 Congruences of Null-Extremals in the calculus of variations. J.Nat.Acad.Math. (India)!, 165–178.

  • 1984 Variational Principles for Field Variables that are subject to Group Actions. In “Differential Topology”, a volume in honor of Marston Morse, Teubner Verlag, Leipzig (29 pages).

  • 1984 Null-Distributions in the calculus of variations of multiple integrals. Math.Colloq. Univ.Cape Town, 13, 57–82.

  • 1984 Gauge Transformations of type (0,2) tensor fields and associated Varational Principles. Quaest.Math.7, 105–140.

  • 1984 A Cartan form for the field theory of Caratheodory in the calculus of variations of multiple integrals. In “Calculus of Variations and Global Analysis”, a volume in honor of L.Euler (Marcel Dekker, N.Y.), (30 pages).

  • 1989 Adapted contact structures and parameter-dependend canonical transformations. To appear in Constantin Caratheodory: an international tribute, Greek Mathematical Society, Athens (1989), 39 pages.

  • 1989 Differential-geometric structures associated with families of r-parameter point transformations. In Geometry and Topology ed. G.M. Stratopoulos, World Sci. Publ.Co., Singapore (1989), 259–280.

  • 1989 Local differential-geometric structures on Lie groups, Tensor (N.S.)48(1989),71–94.

  • 1989 Legendre Transformations and Cartan forms in the calculus of variations of multiple integrals. Part I: Legendre Transformations, Quaest.Math. 12 (1989), 205–229. Part II: Canonical Distributions and Cartan forms, Quaest.Math. 12(1989),315–339

  • 1990 Invariant variational problems on group manifolds. To appear in: Quaest.Math., 40 pages.

  • 1990 Adjoint connections on group manifolds and gauge transformations. in “The Mathematical Heritage of C.F.Gauss”, ed.G.Rassias, World Scientific Publ.Co. Singapore, 1990, 1–24.

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Rund, H. Hanno Rund. Results. Math. 24, 3–11 (1993). https://doi.org/10.1007/BF03322313

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