In this work, we study the Lichnerowicz cohomology of a differentiable manifold M. It is the cohomology of the differential forms on M with the differential of de Rham d deformed by a closed 1-form w, namely, d is replaced by dw = d + w^. This cohomology is very different from the de Rham cohomology when w is not exact. The importance of Lichnerowicz cohomology comes from the fact that it is a tool adapted to the study of the locally conformal symplectic manifolds. It also intervenes in the study of Riemannian flows. We give a complete proof of Kunneth formula and we use this formula to find new examples of trivial and nontrivial Lichnerowicz cohomology groups. We also prove the Leray-Hirsch theorem for Lichnerowicz cohomology. This Theorem is a generalization of the Kunneth formula to fiber bundles. We introduce the Lichnerowicz basic cohomology and use the Gysin exact sequence of Riemannian flow F on a differentiable manifold M to calculate the Lichnerowicz basic cohomology H_w(M,F) where w is the mean curvature form of the flow F.
|Author||Hassan AIT HADDOU|
|Number of Pages||84|
|Country of Manufacture||India|
|Product Brand||LAP LAMBERT Academic Publishing|
|Product Packaging Info||Box|
|In The Box||1 Piece|
|Product First Available On ClickOnCare.com||2015-07-29 00:00:00|