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T-Parallel Fields and Mixed Curvature

  • Vladimir Y. Rovenskii

Abstract

The study of the first and second variations of the length or the energy of curves in a Riemannian manifold leads to the Jacobi equation. Sometimes the simple use of the second variation allows us to establish relationships between curvature properties and the structure of a manifold in general. We’ll give some basic material from the variational theory of geodesics; for more details see [KN], [BuZ] and [GHL].

Keywords

Vector Field Riemannian Manifold Sectional Curvature Riccati Equation Jacobi Equation 
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

© Birkhäuser Boston 1998

Authors and Affiliations

  • Vladimir Y. Rovenskii
    • 1
  1. 1.Mathematics Department/Geometry ChairPedagogical InstituteRussia

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