Abstract
In this paper, we consider an n-dimensional compact Riemannian manifold (M,g) of constant scalar curvature and show that the presence of a non-Killing conformal vector field ξ on M that is also an eigenvector of the Laplacian operator acting on smooth vector fields with eigenvalue λ together with a condition on Ricci curvature of M, that the Ricci curvature in the direction of a certain vector field is greater than or equal to (n − 1)λ, forces M to be isometric to the n-sphere S n(λ).
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This Work is supported by King Saud University, Deanship of Scientific Research, College of Science Research Center.
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Deshmukh, S. Conformal Vector Fields and Eigenvectors of Laplacian Operator. Math Phys Anal Geom 15, 163–172 (2012). https://doi.org/10.1007/s11040-012-9106-x
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DOI: https://doi.org/10.1007/s11040-012-9106-x