Local Riemannian Geometry of Foliations

  • Vladimir Y. Rovenskii


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:
$$ B_1 \left( {y,x} \right) = P_1 \left( {\nabla _x y} \right),{\text{ }}B_2 \left( {x,y} \right) = P_2 \left( {\nabla _y x} \right), $$
were P i : TMT i (i = 1, 2) are orthoprojectors.


Riemannian Manifold Sectional Curvature Fundamental Form Warped Product Riemannian Foliation 
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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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