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Geometry of Lagrangian Submanifolds Related to Isoparametric Hypersurfaces

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

Abstract

In this article we shall provide a survey of our recent works and their environs on differential geometry of Lagrangian submanifolds in specific Kähler manifolds such as complex projective spaces, complex space forms, Hermitian symmetric spaces and so on. We shall emphasis on the relationship between certain minimal Lagrangian submanifold in complex hyperquadrics and isoparametric hypersurfaces in spheres. We shall discuss their properties and related problems of the Gauss images of isoparametric hypersurfaces. This article is mainly based on my joint work with Hui Ma (Tsinghua University, Beijing).

Keywords

Complex Projective Space Lagrangian Submanifolds Hermitian Symmetric Space Isoparametric Hypersurface Gauss Image 
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.

Notes

Acknowledgements

The author sincerely would like to thank Professor Young Jin Suh for leading the international joint project of submanifold theory in differential geometry and Professor Jürgen Berndt for his valuable suggestion and his interest in this work.

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Osaka City University Advanced Mathematical Institute (OCAMI) & Department of MathematicsOsaka City UniversityOsakaJapan

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