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Three dimensional critical point of the total scalar curvature
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It has been conjectured that, on a compact 3-dimensional ori- entable manifold, a critical point of the total scalar curvature restricted to the space of constant scalar curvature metrics of unit volume is Einstein. In this paper we prove this conjecture under a condition that ker s′∗ g 6≠ 0, which generalizes the previous partial results.
Abstract
It has been conjectured that, on a compact 3-dimensional ori- entable manifold, a critical point of the total scalar curvature restricted to the space of constant scalar curvature metrics of unit volume is Einstein. In this paper we prove this conjecture under a condition that ker s′∗ g 6≠ 0, which generalizes the previous partial results.
참고문헌 (7)
- A. L. Besse, "Einstein Manifolds" (1987), Springer-Verlag
- 장정욱, "CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE", 대한수학회보, 49(3), pp.655~667 (2012), 대한수학회
- A. E. Fischer, "Manifolds of Riemannian metrics with prescribed scalar curvature", Bull. Amer. Math. Soc, 80, pp.479~484 (1974)
- S. Hwang, "The critical point equation on a three dimensional compact manifold", Proc. Amer. Math. Soc, 131(10), pp.3221~3230 (2003)
- 황승수, "Some remarks on stable minimal surfaces in the critical point of the total scalar curvature", 대한수학회논문집, 23(4), pp.587~595 (2008), 대한수학회
- S. Hwang, "Rigidity of the critical point equation", Math. Nachr, 283(6), pp.846~853 (2010)
- M. Obata, "Certain conditions for a Riemannian manifold to be isometric with a sphere", J. Math. Soc. Japan, 14(3), pp.333~340 (1962)
관련 논문AI추천
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