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"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.
Inhaltsverzeichnis
Randers Spaces.- Randers Metrics and Geodesics.- Randers Metrics of Isotropic S-Curvature.- Riemann Curvature and Ricci Curvature.- Projective Geometry of Randers Spaces.- Randers Metrics with Special Riemann Curvature Properties.- Randers Metrics of Weakly Isotropic Flag Curvature.-Projectively Flat Randers Metrics.- Conformal Geometry of Randers Metrics.- Dually Flat Randers Metrics
Bericht
From the book reviews:
"The book under review is concerned with the simplest non-Riemannian Finsler metrics: the Randers metrics. It contains the most important results about this kind of Finsler metrics obtained in recent years. ... this text is a treasure for every researcher interested in Finsler geometry." (Rafael Santamaría, Mathematical Reviews, April, 2014)
