Geometriae Dedicata

, Volume 29, Issue 3, pp 259–277 | Cite as

Isometric, holomorphic and symplectic reflections

  • B. Y. Chen
  • L. Vanhecke
Article

Abstract

As an extension of local geodesic symmetries we study here local reflections with respect to a topologically embedded submanifoldP in a Riemannian manifold (M, g). First we derive a criterion for isometric reflections. Then we study holomorphic and symplectic reflections on an almost Hermitian manifold. In particular we focus on the influence of these reflections on the intrinsic and extrinsic geometry of the submanifold. Finally we treat these three kinds of reflections and their relationship when the ambient manifold is a locally Hermitian symmetric space. The results are derived by the use of Jacobi vector fields.

Keywords

Riemannian Manifold Symmetric Space Hermitian Manifold Hermitian Symmetric Space Geodesic Submanifold 

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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • B. Y. Chen
    • 1
  • L. Vanhecke
    • 2
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Department of MathematicsKatholieke Universiteit LeuvenLeuvenBelgium

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