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Journal Articles Pacific Journal of Mathematics Year : 2013

Thin r-neighborhoods of embedded geodesics with finite length and negative Jacobi operator are strongly convex

Philippe Delanoë

Abstract

In a complete Riemannian manifold, an embedded geodesic γ with finite length and negative Jacobi operator admits an r-neighborhood Nr(γ) with radius r > 0 small enough such that each couple of points of Nr(γ) can be joined by a unique geodesic contained in Nr(γ) where it minimizes length among the piecewise C1 paths joining its end points.
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Dates and versions

hal-00824701 , version 1 (22-05-2013)

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Philippe Delanoë. Thin r-neighborhoods of embedded geodesics with finite length and negative Jacobi operator are strongly convex. Pacific Journal of Mathematics, 2013, 264 (2), pp.307-331. ⟨10.2140/pjm.2013.264.307⟩. ⟨hal-00824701⟩
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