Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on Fischer-Marsden's conjecture

Author: Ying Shen
Journal: Proc. Amer. Math. Soc. 125 (1997), 901-905
MSC (1991): Primary 53C21, 53C42
MathSciNet review: 1353399
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C21, 53C42

Retrieve articles in all journals with MSC (1991): 53C21, 53C42

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

Received by editor(s): June 12, 1995
Communicated by: Peter Li
Article copyright: © Copyright 1997 American Mathematical Society