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A note on Fischer-Marsden's conjecture
Author(s):
Ying
Shen
Journal:
Proc. Amer. Math. Soc.
125
(1997),
901-905.
MSC (1991):
Primary 53C21, 53C42
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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:
10.1090/S0002-9939-97-03635-6
PII:
S 0002-9939(97)03635-6
Received by editor(s):
June 12, 1995
Communicated by:
Peter Li
Copyright of article:
Copyright
1997,
American Mathematical Society
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