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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on Fischer-Marsden’s conjecture
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by Ying Shen PDF
Proc. Amer. Math. Soc. 125 (1997), 901-905 Request permission

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