A note on Fischer-Marsden's conjecture |
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| Authors: | Ying Shen |
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| Institution: | Department of Mathematics, Texas A & M University, College Station, Texas 77843 |
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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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