k-parameter geodesic variations

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Bucataru, Ioan²  Dahl, Matias F.¹ 

[1] Aalto Univ, Inst Math, FI-00076 Aalto, Finland

[2] Alexandru Ioan Cuza Univ, Fac Math, Iasi 700506, Romania

关键词: Semispray;    Jacobi equation;    Geodesic variation;    Jacobi tensor;    Shape operator;    Riccati equation;   

DOI  :  10.1016/j.geomphys.2012.06.006

来源: Elsevier

【 摘 要 】

Suppose S is a semispray on a manifold M. We know that the complete lift S-c of S is a semispray on TM with the property that geodesics of S-c correspond to Jacobi fields of S. In this note we generalise this result and show how geodesic variations of k variables are related to geodesics of the kth iterated complete lift of S. Moreover, for sprays (that is, homogeneous semisprays) we show how geodesic variations of (n-1) variables are related to a natural generalisation of Jacobi tensors. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free