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Conformal Transformations Between Complete Product Riemannian Manifolds

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Real and Complex Submanifolds

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 106))

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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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References

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Institute of Natural Sciences, Kyung Hee University, Yong-In, 446-701, Republic of Korea

    Byung Hak Kim

Authors
  1. Byung Hak Kim
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Correspondence to Byung Hak Kim .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Kyungpook National University, Daegu, Republic of Korea

    Young Jin Suh

  2. Department of Mathematics, King’s College London, London, UK

    Jürgen Berndt

  3. Department of Mathematics, Osaka City University, Osaka, Japan

    Yoshihiro Ohnita

  4. Department of Applied Mathematics, Kyung Hee University, Yongin, Republic of Korea

    Byung Hak Kim

  5. The Center for Geometry and its Applications, Pohang University of Science and Technology, Pohang, Republic of Korea

    Hyunjin Lee

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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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