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Geometriae Dedicata

, Volume 90, Issue 1, pp 115–125 | Cite as

The Totally Geodesic Coisotropic Submanifolds in Kähler Manifolds

  • Xu Cheng
Article

Abstract

In this paper, we consider the coisotropic submanifolds in a Kähler manifold of nonnegative holomorphic curvature. We prove an intersection theorem for compact totally geodesic coisotropic submanifolds and discuss some topological obstructions for the existence of such submanifolds. Our results apply to Lagrangian submanifolds and real hypersurfaces since the class of coisotropic submanifolds includes them. As an application, we give a fixed-point theorem for compact Kähler manifolds with positive holomorphic curvature. Also, our results can be further extended to nearly Kähler manifolds.

Kähler manifold coisotropic submanifold holomorphic curvature 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Xu Cheng
    • 1
  1. 1.IMPARio de JaneiroBrazil

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