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Finsler Geometry
 
Edited by: David Bao University of Houston, Houston, TX
Shiing-shen Chern University of California, Berkeley, Berkeley, CA
Zhongmin Shen Indiana-Purdue University at Indianapolis, Indianapolis, IN
Finsler Geometry
Softcover ISBN:  978-0-8218-0507-7
Product Code:  CONM/196
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7787-6
Product Code:  CONM/196.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-0507-7
eBook: ISBN:  978-0-8218-7787-6
Product Code:  CONM/196.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Finsler Geometry
Click above image for expanded view
Finsler Geometry
Edited by: David Bao University of Houston, Houston, TX
Shiing-shen Chern University of California, Berkeley, Berkeley, CA
Zhongmin Shen Indiana-Purdue University at Indianapolis, Indianapolis, IN
Softcover ISBN:  978-0-8218-0507-7
Product Code:  CONM/196
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7787-6
Product Code:  CONM/196.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-0507-7
eBook ISBN:  978-0-8218-7787-6
Product Code:  CONM/196.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1961996; 310 pp
    MSC: Primary 53

    This volume features proceedings from the 1995 Joint Summer Research Conference on Finsler Geometry (Seattle, WA), chaired by S.S. Chern and co-chaired by D. Bao and Z. Shen.

    The editors of this volume have provided comprehensive and informative “capsules” of presentations and technical reports. This was facilitated by classifying the papers into the following 6 separate sections—3 of which are applied and 3 are pure:

    • Finsler Geometry over the reals
    • Complex Finsler geometry
    • Generalized Finsler metrics
    • Applications to biology, engineering, and physics
    • Applications to control theory
    • Applications to relativistic field theory

    Each section contains a preface that provides a coherent overview of the topic and includes an outline of the current directions of research and new perspectives. A short list of open problems concludes each contributed paper.

    A number of photos are featured in the volume, for example, that of Finsler. In addition, conference participants are also highlighted.

    Readership

    : Graduate students, research mathematicians, physicists, and engineers interested in differential geometry, complex analysis, control theory, and mathematical biology.

  • Table of Contents
     
     
    • Section 1: Finsler Geometry over the Reals [ MR 1403571 ]
    • 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 [ MR 1403571 ]
    • 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 [ MR 1403571 ]
    • 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 [ MR 1403571 ]
    • 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 [ MR 1403571 ]
    • 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 [ MR 1403571 ]
    • 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 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1961996; 310 pp
MSC: Primary 53

This volume features proceedings from the 1995 Joint Summer Research Conference on Finsler Geometry (Seattle, WA), chaired by S.S. Chern and co-chaired by D. Bao and Z. Shen.

The editors of this volume have provided comprehensive and informative “capsules” of presentations and technical reports. This was facilitated by classifying the papers into the following 6 separate sections—3 of which are applied and 3 are pure:

  • Finsler Geometry over the reals
  • Complex Finsler geometry
  • Generalized Finsler metrics
  • Applications to biology, engineering, and physics
  • Applications to control theory
  • Applications to relativistic field theory

Each section contains a preface that provides a coherent overview of the topic and includes an outline of the current directions of research and new perspectives. A short list of open problems concludes each contributed paper.

A number of photos are featured in the volume, for example, that of Finsler. In addition, conference participants are also highlighted.

Readership

: Graduate students, research mathematicians, physicists, and engineers interested in differential geometry, complex analysis, control theory, and mathematical biology.

  • Section 1: Finsler Geometry over the Reals [ MR 1403571 ]
  • 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 [ MR 1403571 ]
  • 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 [ MR 1403571 ]
  • 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 [ MR 1403571 ]
  • 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 [ MR 1403571 ]
  • 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 [ MR 1403571 ]
  • 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 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.