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Conformal Transformations Between Complete Product Riemannian Manifolds

  • Byung Hak Kim
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)

Abstract

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.

Keywords

Riemannian Manifold Product Structure Conformal Transformation Einstein Manifold Complete Riemannian Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Institute of Natural SciencesKyung Hee UniversityYong-InRepublic of Korea

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