# Finsler Geometry

### About this Title

**David Bao**, **Shiing-shen Chern** and **Zhongmin Shen**, Editors

Publication: Contemporary Mathematics

Publication Year
1996: Volume 196

ISBNs: 978-0-8218-0507-7 (print); 978-0-8218-7787-6 (online)

DOI: http://dx.doi.org/10.1090/conm/196

MathSciNet review: 1403571

### Table of Contents

**Front/Back Matter**

** Section 1: Finsler Geometry over the Reals **

- D. Bao, S. S. Chern and Z. Shen – Preface for “Finsler geometry over the reals” [MR 1403572]
- David Bao, S. S. Chern and Z. Shen – On the Gauss-Bonnet integrand for $4$-dimensional Landsberg spaces [MR 1403573]
- Robert L. Bryant – Finsler structures on the $2$-sphere satisfying $K=1$ [MR 1403574]
- G. D. Chakerian – Integral geometry in Minkowski spaces [MR 1403575]
- Shiing-shen Chern – Riemannian geometry as a special case of Finsler geometry [MR 1403576]
- Francis J. Flaherty – Dirac operators for Finsler spaces [MR 1403577]
- David Bao and Brad Lackey – Special eigenforms on the sphere bundle of a Finsler manifold [MR 1403578]
- Makoto Matsumoto – Remarks on Berwald and Landsberg spaces [MR 1403579]
- Zhongmin Shen – Finsler manifolds of constant positive curvature [MR 1403580]

** Section 2: Complex Finsler Geometry **

- M. Abate, T. Aikou and G. Patrizio – Preface for “Complex Finsler geometry” [MR 1403581]
- Marco Abate and Giorgio Patrizio – Finsler metrics of constant curvature and the characterization of tube domains [MR 1403582]
- Tadashi Aikou – Some remarks on locally conformal complex Berwald spaces [MR 1403583]
- John Bland and Morris Kalka – Variations of holomorphic curvature for Kähler Finsler metrics [MR 1403584]
- James J. Faran, V – The equivalence problem for complex Finsler Hamiltonians [MR 1403585]
- Shoshichi Kobayashi – Complex Finsler vector bundles [MR 1403586]

** Section 3: Generalized Finsler Metrics **

- Mihai Anastasiei and Radu Miron – Preface for “Generalized Finsler metrics” [MR 1403587]
- Mihai Anastasiei – Certain generalizations of Finsler metrics [MR 1403588]
- Mihai Anastasiei – A historical remark on the connections of Chern and Rund [MR 1403589]
- L. Kozma – On Landsberg spaces and holonomy of Finsler manifolds [MR 1403590]
- Radu Miron – Some problems in the geometries of Finsler type [MR 1403591]

** Section 4: Applications to Biology, Engineering, and Physics **

- P. L. Antonelli – Preface for “Applications of Finsler differential geometry to biology, engineering, and physics” [MR 1403592]
- P. L. Antonelli, M. Matsumoto and T. J. Zastawniak – On $y$-Berwald spaces of dimension two and associated heterochronic systems with Finslerian noise [MR 1403593]
- Roman S. Ingarden – On physical applications of Finsler geometry [MR 1403594]

** Section 5: Applications to Control Theory **

- Robert B. Gardner and George R. Wilkens – Preface for “Applications of Finsler geometry to control theory” [MR 1403595]
- Robert B. Gardner and George R. Wilkens – A pseudo-group isomorphism between control systems and certain generalized Finsler structures [MR 1403596]
- George R. Wilkens – Finsler geometry in low-dimensional control theory [MR 1403597]

** Section 6: Applications to Relativistic Field Theory **

- R. G. Beil – Preface for “Applications of Finsler geometry to relativistic field theory” [MR 1403598]
- R. G. Beil – Finsler geometry and a unified field theory [MR 1403599]
- Howard E. Brandt – Finslerian spacetime [MR 1403600]
- Solange F. Rutz – Symmetry in Finsler spaces [MR 1403601]
- Jose G. Vargas and Douglas G. Torr – Elementary geometries underlying the theory of Euclidean connections on Finsler metrics of Lorentzian signature [MR 1403602]