Ebook: Finsler Geometry: An Approach via Randers Spaces
- Tags: Differential Geometry, Geometry, Mathematical Methods in Physics
- Year: 2012
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
"Finsler Geometry: An Approach via Randers Spaces" exclusively deals with a special class of Finsler metrics -- Randers metrics, which are defined as the sum of a Riemannian metric and a 1-form. Randers metrics derive from the research on General Relativity Theory and have been applied in many areas of the natural sciences. They can also be naturally deduced as the solution of the Zermelo navigation problem. The book provides readers not only with essential findings on Randers metrics but also the core ideas and methods which are useful in Finsler geometry. It will be of significant interest to researchers and practitioners working in Finsler geometry, even in differential geometry or related natural fields.
Xinyue Cheng is a Professor at the School of Mathematics and Statistics of Chongqing University of Technology, China. Zhongmin Shen is a Professor at the Department of Mathematical Sciences of Indiana University Purdue University, USA.
"Finsler Geometry: An Approach via Randers Spaces" exclusively deals with a special class of Finsler metrics -- Randers metrics, which are defined as the sum of a Riemannian metric and a 1-form. Randers metrics derive from the research on General Relativity Theory and have been applied in many areas of the natural sciences. They can also be naturally deduced as the solution of the Zermelo navigation problem. The book provides readers not only with essential findings on Randers metrics but also the core ideas and methods which are useful in Finsler geometry. It will be of significant interest to researchers and practitioners working in Finsler geometry, even in differential geometry or related natural fields.
Xinyue Cheng is a Professor at the School of Mathematics and Statistics of Chongqing University of Technology, China. Zhongmin Shen is a Professor at the Department of Mathematical Sciences of Indiana University Purdue University, USA.
"Finsler Geometry: An Approach via Randers Spaces" exclusively deals with a special class of Finsler metrics -- Randers metrics, which are defined as the sum of a Riemannian metric and a 1-form. Randers metrics derive from the research on General Relativity Theory and have been applied in many areas of the natural sciences. They can also be naturally deduced as the solution of the Zermelo navigation problem. The book provides readers not only with essential findings on Randers metrics but also the core ideas and methods which are useful in Finsler geometry. It will be of significant interest to researchers and practitioners working in Finsler geometry, even in differential geometry or related natural fields.
Xinyue Cheng is a Professor at the School of Mathematics and Statistics of Chongqing University of Technology, China. Zhongmin Shen is a Professor at the Department of Mathematical Sciences of Indiana University Purdue University, USA.
Content:
Front Matter....Pages i-viii
Randers Spaces....Pages 1-12
Randers Metrics and Geodesics....Pages 13-25
Randers Metrics of Isotropic S-Curvature....Pages 27-49
Riemann Curvature and Ricci Curvature....Pages 51-59
Projective Geometry of Randers Spaces....Pages 61-75
Randers Metrics with Special Riemann Curvature Properties....Pages 77-89
Randers Metrics of Weakly Isotropic Flag Curvature....Pages 91-109
Projectively Flat Randers Metrics....Pages 111-125
Conformal Geometry of Randers Metrics....Pages 127-135
Dually Flat Randers Metrics....Pages 137-147
Back Matter....Pages 149-150
"Finsler Geometry: An Approach via Randers Spaces" exclusively deals with a special class of Finsler metrics -- Randers metrics, which are defined as the sum of a Riemannian metric and a 1-form. Randers metrics derive from the research on General Relativity Theory and have been applied in many areas of the natural sciences. They can also be naturally deduced as the solution of the Zermelo navigation problem. The book provides readers not only with essential findings on Randers metrics but also the core ideas and methods which are useful in Finsler geometry. It will be of significant interest to researchers and practitioners working in Finsler geometry, even in differential geometry or related natural fields.
Xinyue Cheng is a Professor at the School of Mathematics and Statistics of Chongqing University of Technology, China. Zhongmin Shen is a Professor at the Department of Mathematical Sciences of Indiana University Purdue University, USA.
Content:
Front Matter....Pages i-viii
Randers Spaces....Pages 1-12
Randers Metrics and Geodesics....Pages 13-25
Randers Metrics of Isotropic S-Curvature....Pages 27-49
Riemann Curvature and Ricci Curvature....Pages 51-59
Projective Geometry of Randers Spaces....Pages 61-75
Randers Metrics with Special Riemann Curvature Properties....Pages 77-89
Randers Metrics of Weakly Isotropic Flag Curvature....Pages 91-109
Projectively Flat Randers Metrics....Pages 111-125
Conformal Geometry of Randers Metrics....Pages 127-135
Dually Flat Randers Metrics....Pages 137-147
Back Matter....Pages 149-150
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