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.
| Autorius: | Hassan Ait Haddou |
| Leidėjas: | LAP LAMBERT Academic Publishing |
| Išleidimo metai: | 2010 |
| Knygos puslapių skaičius: | 84 |
| ISBN-10: | 3843364672 |
| ISBN-13: | 9783843364676 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Geometry |
Parašykite atsiliepimą apie „From symplectic and contact geometry to dynamical systems: The Lichnerowicz cohomology as an intersting generalisation of De Rham usual cohomology“
