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Softcover ISBN:  9780821805077 
Product Code:  CONM/196 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821877876 
Product Code:  CONM/196.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821805077 
eBook ISBN:  9780821877876 
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 DetailsContemporary MathematicsVolume: 196; 1996; 310 ppMSC: Primary 53
This volume features proceedings from the 1995 Joint Summer Research Conference on Finsler Geometry (Seattle, WA), chaired by S.S. Chern and cochaired 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 GaussBonnet 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 ]

Shiingshen 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 pseudogroup isomorphism between control systems and certain generalized Finsler structures [ MR 1403596 ]

George R. Wilkens — Finsler geometry in lowdimensional 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 ]


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This volume features proceedings from the 1995 Joint Summer Research Conference on Finsler Geometry (Seattle, WA), chaired by S.S. Chern and cochaired 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.
: 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 GaussBonnet 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 ]

Shiingshen 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 pseudogroup isomorphism between control systems and certain generalized Finsler structures [ MR 1403596 ]

George R. Wilkens — Finsler geometry in lowdimensional 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 ]