Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

Details Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

2011-12-30

arxiv.org/abs/1201.0147v2

Mathematics

Differential Geometry

14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition correc

Scientific paper

Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.

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