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A note on Fischer-Marsden's conjecture


Author: Ying Shen
Journal: Proc. Amer. Math. Soc. 125 (1997), 901-905
MSC (1991): Primary 53C21, 53C42
DOI: https://doi.org/10.1090/S0002-9939-97-03635-6
MathSciNet review: 1353399
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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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Ying Shen
Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843
Address at time of publication: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
Email: yshen@math.tamu.edu, ying.shen@dartmouth.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03635-6
Received by editor(s): June 12, 1995
Communicated by: Peter Li
Article copyright: © Copyright 1997 American Mathematical Society