Публикации

A selfsimilar 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 Euclidean space. A radiant Hessian manifold is a selfsimilar Hessian manifold (M,∇,g,ξ) such that ∇ξ=λId, where λ 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.