On Static Manifolds and Related Critical Spaces with cyclic parallel Ricci tensor

Autor:	da Silva, Adam, Baltazar, Halyson
Rok vydání:	2018
Předmět:	Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	The aim of this paper is to classify three dimensional compact Riemannian manifolds $(M^{3},g)$ that admits a non-constant solution to the equation $$-\Delta f g+Hess f-fRic=\mu Ric+\lambda g,$$ for some special constants $(\mu, \lambda)$, under assumption that the manifold has cyclic parallel Ricci tensor. Namely, the structures that we will study here will be: positive static triples, critical metrics of the volume functional, and critical metrics of the total scalar curvature functional. We shall also classify $n$-dimensional critical metrics of the volume functional with non-positive scalar curvature and satisfying the cyclic parallel Ricci tensor condition. Comment: 15 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1811.04447 Zobrazit plný text záznamu View this record from Arxiv