Submanifolds of Kähler and Sasakian Manifolds

  • David E. Blair
Part of the Progress in Mathematics book series (PM, volume 203)


In this chapter we study submanifolds in both contact and Kähler geometry. These are extensive subjects in their own right and we give only a few basic results. For a submanifold M of a Riemannian manifold (, ) we denote the induced metric by g. Then the Levi-Cività connection ∇ of g and the second fundamental form σ are related to the ambient Levi-Cività connection ∇̃ by
$${\bar\nabla_X}Y = {\nabla_X}Y +\sigma(X,Y)$$


Sectional Curvature Fundamental Form Constant Curvature Lagrangian Submanifold Sasakian Manifold 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • David E. Blair
    • 1
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

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