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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 
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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 ]