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The critical point equation on a four dimensional warped product manifold
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Abstract
On a compact oriented n-dimensional manifold (Mn ;g), it has been conjectured that a metricg satisfying the criticalpoint equation (2) should be Einstein. In this paper, we prove thatif a manifold (M4;g) is a 4-dimensional oriented compact warpedproduct, then g can not be a solution of CPE with a non-zerosolution function f.
참고문헌 (9)
- "Einstein Manifolds" (1987), Springer-Verlag
- "Une stratication de l'espace des structures riemanniennes", 30, pp.1~41 (1975)
- "Manifolds of Riemannian metrics with pre-scribed scalar curvature", 80, pp.479~484 (1974)
- "Critical points of the total scalar curvature functionals on the spaceof metrics of constant scalar curvature", 103(2), pp.135~142 (2000)
- "The critical point equation on a thre dimensional compact manifold", 131(10), pp.3221~3230 (2003)
- "Critical points and warped product metrics", 41(1), pp.117~123 (2004)
- "Curvature functions for open2 manifolds", pp.219~ (1974)
- "Certain conditions for a Riemannian manifold to be isometric with a"
- "Certain conditions for a Riemannian manifold to be isometric with a"
관련 논문AI추천
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