Randers Metrics and Geodesics

Xinyue Cheng () and Zhongmin Shen ()
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Xinyue Cheng: Chongqing University of Technology, School of Mathematics and Statistics
Zhongmin Shen: Indiana University-Purdue University Indianapolis (IUPUI), Department of Mathematical Sciences

Chapter Chapter 2 in Finsler Geometry, 2012, pp 13-25 from Springer

Abstract: Abstract Let M be an n-dimensional manifold. For a point x ∈ M, let T x M denote the tangent space at x. The tangent bundle $$ TM: = \bigcup\limits_{x \in M} {T_x M} $$ consists of all tangent vectors on M with natural manifold structure. We denote elements in TM by (x, y), where y ∈ T x M. If (x i ) is a local coordinate system in M, then $$ \left\{ {\frac{\partial } {{\partial x^i }}} \right\}$$ is a local natural basis for TM. It induces a standard local coordinate system (x i , y i ) in TM by $$ \left. {y = y^i \frac{\partial } {{\partial x^i }}} \right|_x $$ . We shall not distinguish between x and its coordinates (x i ) and (x, y) and its coordinates (x i , y i ) in the standard local coordinate system in TM.

Keywords: Finsler Manifold; Finsler Metrics; Navigation Data; Navigation Problem; Minkowski Norm (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-3-642-24888-7_2

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