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

Author

Listed:
  • Amira Ishan

    (Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Sharief Deshmukh

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Gabriel-Eduard Vîlcu

    (Department of Cybernetics, Economic Informatics, Finance and Accountancy, Petroleum-Gas University of Ploieşti, Bd. Bucureşti 39, 100680 Ploieşti, Romania)

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 S m ( 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.

Suggested Citation

  • Amira Ishan & Sharief Deshmukh & Gabriel-Eduard Vîlcu, 2021. "Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold," Mathematics, MDPI, vol. 9(8), pages 1-9, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:863-:d:536079
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