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

2021/12/21 by António Freitas, Freitas, Antônio, Israel Evangelista +3
Engineering · Mathematics · #53A30 #53C20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2112.11220

openalex publication_date 2021/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (Mⁿ,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 (Mⁿ,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 \mathbbSⁿ₊(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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