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The Fixed Point Set of a Holomorphic Isometry and the Intersection of Two Real Forms in the Complex Grassmann Manifold

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Book cover Real and Complex Submanifolds

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

Abstract

We study the fixed point set of a holomorphic isometry of the complex Grassmann manifold and the intersection of two real forms which are congruent to the real Grassmann manifold. Furthermore, we investigate the relation between them.

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Acknowledgements

The first author was partly supported by the Grant-in-Aid for Science Research (C) 2013 (No. 25400070), Japan Society for the Promotion of Science. The second author was partly supported by the Grant-in-Aid for Science Research (C) 2013 (No. 23540108), Japan Society for the Promotion of Science. The third author was partly supported by the Grant-in-Aid for Science Research (C) 2013 (No. 24540064), Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. Faculty of Arts and Sciences, Department of Mathematics and Physical Sciences, Kyoto Institute of Technology, Matsugasaki, Sakyoku, Kyoto, 606-8585, Japan

    Osamu Ikawa

  2. Faculty of Science and Technology, Department of Mathematics, Tokyo University of Science, Noda, Chiba, 278-8510, Japan

    Makiko Sumi Tanaka

  3. Faculty of Pure and Applied Sciences, Division of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan

    Hiroyuki Tasaki

Authors
  1. Osamu Ikawa
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  2. Makiko Sumi Tanaka
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  3. Hiroyuki Tasaki
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Corresponding author

Correspondence to Makiko Sumi Tanaka .

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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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Ikawa, O., Tanaka, M.S., Tasaki, H. (2014). The Fixed Point Set of a Holomorphic Isometry and the Intersection of Two Real Forms in the Complex Grassmann Manifold. 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_28

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