A note on Fischer-Marsden’s conjecture

Shen, Ying

doi:10.1090/S0002-9939-97-03635-6

A note on Fischer-Marsden’s conjecture
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by Ying Shen

Proc. Amer. Math. Soc. 125 (1997), 901-905

DOI: https://doi.org/10.1090/S0002-9939-97-03635-6

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Abstract:

In this paper, we borrowed some ideas from general relativity and find a Robinson-type identity for the overdetermined system of partial differential equations in the Fischer-Marsden conjecture. We proved that if there is a nontrivial solution for such an overdetermined system on a 3-dimensional, closed manifold with positive scalar curvature, then the manifold contains a totally geodesic 2-sphere.

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