Relative radial mass and rigidity of some warped product manifolds

Details Relative radial mass and rigidity of some warped product manifolds Relative radial mass and rigidity of some warped product manifolds

2008-02-22

arxiv.org/abs/0802.3270v1

Mathematics

Differential Geometry

14 pages

Scientific paper

We give a Riccati type formula adapted for two metrics having the same geodesics rays starting from a point or orthogonal to an hypersurface, one of these metrics being a warped product if the dimension $n$ is greater than or equal to 3. This formula has non-trivial geometric consequences such as a positive mass type theorem and other rigidity results. We also apply our result to some standard models.

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