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Local Riemannian Geometry of Foliations

  • Vladimir Y. Rovenskii

Abstract

For two arbitrary complementary orthogonal distributions T1 and T2 on TM, we define the structural tensors B1 : T2 × T1T1 and B2 : T1 × T2T2 by the following formulas:
$$ B_1 \left( {y,x} \right) = P_1 \left( {\nabla _x y} \right),{\text{ }}B_2 \left( {x,y} \right) = P_2 \left( {\nabla _y x} \right), $$
(2.1)
were P i : TMT i (i = 1, 2) are orthoprojectors.

Keywords

Riemannian Manifold Sectional Curvature Fundamental Form Warped Product Riemannian Foliation 
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.

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Copyright information

© Birkhäuser Boston 1998

Authors and Affiliations

  • Vladimir Y. Rovenskii
    • 1
  1. 1.Mathematics Department/Geometry ChairPedagogical InstituteRussia

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