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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Pseudo-Riemannian manifolds with totally geodesic bisectors


Author: John K. Beem
Journal: Proc. Amer. Math. Soc. 49 (1975), 212-215
MSC: Primary 53B30
DOI: https://doi.org/10.1090/S0002-9939-1975-0362111-4
MathSciNet review: 0362111
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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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DOI: https://doi.org/10.1090/S0002-9939-1975-0362111-4
Article copyright: © Copyright 1975 American Mathematical Society