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Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold
Journal article   Open access  Peer reviewed

Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold

Amira Ishan, Sharief Deshmukh and Gabriel-Eduard Vilcu
Mathematics (Basel), Vol.9(8), p.863
01/04/2021
DOI: https://doi.org/10.3390/math9080863

Abstract

Mathematics Physical Sciences Science & Technology
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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https://doi.org/10.3390/math9080863View
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