Conformal Transformations Between Complete Product Riemannian Manifolds
Nagano proved that if the non-homothetic conformal transformation between complete Riemannian manifolds with parallel Ricci tensor is admitted, then the manifolds are irreducible and isometric to a sphere. From this result and other reasons, it is natural to ask for the problem that does there exist globally a non-homothetic conformal transformation between complete product Riemannian manifolds? In this talk, we introduce and consider about this question and related topics.
KeywordsRiemannian Manifold Product Structure Conformal Transformation Einstein Manifold Complete Riemannian Manifold