Beschreibung
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.
Autorenporträt
EMPLOYMENT EXPERIENCES Since December 2008 -Research Professor,Toulouse Research Institute on Computer Science (IRIT) Toulouse, France 2008, Research at French National Institute of Research on Transport and Security, Lille France 2005-2007 Postdoctoral research at Pure and Applied Mathematics Laboratory, University of Valenciennes, France
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