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A class of non-compact homogeneous Lagrangian submanifolds in complex hyperbolic spaces

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Abstract

We study homogeneous Lagrangian submanifolds in complex hyperbolic spaces. We show there exists a correspondence between compact homogeneous Lagrangian submanifolds in \(\mathbb {C}H^{n}\) and the ones in \(\mathbb {C}^n\), or equivalently, in \(\mathbb {C}P^{n-1}\). Furthermore, we construct and classify non-compact homogeneous Lagrangian submanifolds in \(\mathbb {C}H^n\) obtained by the actions of connected closed subgroups of the solvable part of the Iwasawa decomposition.

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Acknowledgments

The authors would like to thank Jürgen Berndt, Yoshihiro Ohnita, Hiroshi Tamaru and Takayuki Okuda for helpful comments, suggestions and variable discussions. This work was finished while the second author was staying at King’s College London by the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers Mathematical Science of Symmetry, Topology and Moduli, Evolution of International Research Network based on OCAMI?. He is grateful for the hospitality of the college.

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Authors and Affiliations

  1. National Institute of Technology, Kitakyushu College, 5-20-1 Shii, Kokuraminamiku, Kitakyushu, Fukuoka, 802-0985, Japan

    Takahiro Hashinaga

  2. Osaka City University Advanced Mathematical Institute, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

    Toru Kajigaya

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  1. Takahiro Hashinaga
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  2. Toru Kajigaya
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Correspondence to Toru Kajigaya.

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The first author was supported by JSPS KAKENHI Grant Number 16K17603.

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Hashinaga, T., Kajigaya, T. A class of non-compact homogeneous Lagrangian submanifolds in complex hyperbolic spaces. Ann Glob Anal Geom 51, 21–33 (2017). https://doi.org/10.1007/s10455-016-9521-5

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  • DOI: https://doi.org/10.1007/s10455-016-9521-5

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