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.
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Kim, B.H. (2014). Conformal Transformations Between Complete Product Riemannian Manifolds. In: Suh, Y.J., Berndt, J., Ohnita, Y., Kim, B.H., Lee, H. (eds) Real and Complex Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 106. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55215-4_41
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DOI: https://doi.org/10.1007/978-4-431-55215-4_41
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