Selfsimilar Hessian manifolds

2019/08/05 by Osipov, Pavel
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.01731

Abstract

A selfsimiar manifold is a Riemannian manifold (M,g) endowed with a homothetic vector field ξ. We characterize global selfsimilar manifolds and describe the structure of local selfsimilar manifolds. We prove that any selfsimilar manifold with a potential homothetic vector field is a conical Riemannian manifold or a Eucledean space. A radiant Hessian manifold is selfsimilar Hessian manifold (M,∇,g,ξ) such that ∇ξ=λId. We prove that any selfsimilar Hessian manifold with a potential homothetic vector field is locally isomorphic to a product radiant Hessian manifolds and describe the local structure of radiant selfsimialar Hessian manifolds.

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