T-Parallel Fields and Mixed Curvature
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].
KeywordsVector Field Riemannian Manifold Sectional Curvature Riccati Equation Jacobi Equation
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