T-Parallel Fields and Mixed Curvature

  • Vladimir Y. Rovenskii


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].


Vector Field Riemannian Manifold Sectional Curvature Riccati Equation Jacobi Equation 
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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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