THE INTEGRAL OF MIXED SCALAR CURVATURE ALONG A LEAF OF FOLIATION

Vladimir Rovenskii

1991 Math. Subject Classification: 53C12.

Key words: Foliation, distribution, mixed curvature, Riccati equation.

Abstract: By using the method of matrix Riccati ODE, we study Riemannian
manifolds with foliations (distributions), whose mixed Ricci or scalar
curvature is nonnegative and the norms of integrability tensors are bounded
above. We obtain the integral formula for mixed scalar curvature along the
complete leaf, rigidity of totally geodesic distribution, splitting of
foliation with "large" dimension.