Pseudo-Riemannian manifolds with totally geodesic bisectors

Beem, John K.

doi:10.1090/S0002-9939-1975-0362111-4

Pseudo-Riemannian manifolds with totally geodesic bisectors
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by John K. Beem PDF

Proc. Amer. Math. Soc. 49 (1975), 212-215 Request permission

Abstract:

Let $M$ be a pseudo-Riemannian manifold. Locally a distance function may be defined. The bisector of two points is the set of points equidistant from these two points. Our main result is that the bisector of two points which are not zero distance apart is a totally geodesic submanifold of $M$ if and only if $M$ has constant curvature.

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Convex regions in the geometry of paths

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