Randers Metrics and Geodesics

  • Xinyue Cheng
  • Zhongmin Shen


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.


Finsler Manifold Finsler Metrics Navigation Data Navigation Problem Minkowski Norm 
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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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