Selfsimilar Hessian manifolds

A selfsimilar manifold is a Riemannian manifold (M, g) endowed with a homothetic vector field xi. 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 Euclidean space. A radiant Hessian manifold is a selfsimilar Hessian manifold (M, del, g, xi) such that del xi = lambda Id, where lambda is a constant. We prove that any selfsimilar Hessian manifold with a potential homothetic vector field is locally isomorphic to a product of radiant Hessian manifolds and describe the local structure of radiant selfsimilar Hessian manifolds.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This study discusses the properties of selfsimilar manifolds and selfsimilar Hessian manifolds, describing and characterizing the global and local cases.