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

Antônio Freitas; Israel Evangelista; Emanuel Viana

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arXiv · 2112.11220

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

Antônio Freitas·Israel Evangelista·Emanuel Viana

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Abstract

Let $(M^n,g)$ be an $n$-dimensional compact connected Riemannian manifold with boundary. In this article, we study the effects of the presence of a nontrivial conformal vector field on $(M^n,g)$. We used the wekk-known de-Rham Laplace operator and a nontrivial solution of the famous Fischer-Marsden differential equation to provide two characterizations of the hemisphere $\mathbb{S}^{n}_{+}(c)$ 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.

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BibTeX RIS

Antônio Freitas, Israel Evangelista, Emanuel Viana. 2021-12-21. Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold with Boundary. https://arxiv.org/abs/2112.11220

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