Abstract
In this short note we consider an n-dimensional compact Riemannian manifold (M, g) of constant scalar curvature S = n(n − 1)c and show that the presence of a nontrivial conformal vector field ξ on M forces S to be positive. Then we show that an appropriate control on the energy of ξ makes M to be isometric to the n-sphere S n(c).
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This work is supported by the Research center, College of Science, King Saud University.
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Deshmukh, S. Characterizing spheres by conformal vector fields. Ann. Univ. Ferrara 56, 231–236 (2010). https://doi.org/10.1007/s11565-010-0101-5
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DOI: https://doi.org/10.1007/s11565-010-0101-5