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.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- 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