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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Additional Information

**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