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

Autor: Evangelista, Israel, Freitas, Antônio, Viana, Emanuel
Zdroj: Results in Mathematics / Resultate der Mathematik; Dec2022, Vol. 77 Issue 6, p1-14, 14p
Abstrakt: Let (M n , g) be an n-dimensional compact connected Riemannian manifold with smooth boundary. In this article, we study the effects of the presence of a nontrivial conformal vector field on (M n , g) . We used the well-known de-Rham Laplace operator and a nontrivial solution of the famous Fischer–Marsden differential equation to provide two characterizations of the hemisphere S + n (c) of constant curvature c > 0 . As a consequence of the characterization using the Fischer–Marsden equation, we prove the cosmic no-hair conjecture under a given integral condition. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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