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.
https://hal.univ-cotedazur.fr/hal-00824701
Contributor : Philippe Delanoë
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Submitted on : Wednesday, May 22, 2013 - 12:59:26 PM
Last modification on : Friday, January 12, 2018 - 1:51:40 AM
Long-term archiving on: Friday, August 23, 2013 - 4:08:23 AM
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⟩
