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Randers Metrics and Geodesics

  • Xinyue Cheng
  • Zhongmin Shen

Abstract

Let M be an n-dimensional manifold. For a point xM, 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 yT 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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Science Press Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xinyue Cheng
    • 1
  • Zhongmin Shen
    • 2
  1. 1.School of Mathematics and StatisticsChongqing University of TechnologyLijiatuo, ChongqingChina
  2. 2.Department of Mathematical SciencesIndiana University-Purdue University Indianapolis (IUPUI)IndianapolisUSA

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