2021
DOI: 10.3390/math9080863
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Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold

Abstract: We study the effect of a nontrivial conformal vector field on the geometry of compact Riemannian spaces. We find two new characterizations of the m-dimensional sphere Sm(c) of constant curvature c. The first characterization uses the well known de-Rham Laplace operator, while the second uses a nontrivial solution of the famous Fischer–Marsden differential equation.

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Cited by 3 publications
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