Annals of Global Analysis and Geometry

, Volume 11, Issue 2, pp 109–118 | Cite as

Symplectic twistor spaces

  • Alexander G. Reznikov
Article
Received:

Abstract

We introduce some canonical 2-form in the twistor bundles of any Riemannian manifoldM. This form is always closed and turns out to be nondegenerate in the following cases:
  1. 1.

    The curvature ofM is pinched.

     
  2. 2.

    M is an Einstein four-dimensional manifold of positive or negative curvature.

     
  3. 3.

    M is self-dual and the Ricci curvature is pinched.

     

We prove the existence of a large class of compact symplectic manifolds which do not admit any Kählerian structure. Finally, we introduce a Lagrangian lift of a totally geodesic submanifold ofM and apply the Lagrangian intersection methods to totally geodesic submanifolds.

Key words

Twistor bundles symplectic forms Lagrangian lift 

MSC 1991

53 C 57 
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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Alexander G. Reznikov
    • 1
  1. 1.Department of MathematicsHebrew University Giv'at RamJerusalemIsrael

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