From symplectic and contact geometry to dynamical systems: The Lichnerowicz cohomology as an intersting generalisation of De Rham usual cohomology - Couverture souple

AIT HADDOU, Hassan

 
9783843364676: From symplectic and contact geometry to dynamical systems: The Lichnerowicz cohomology as an intersting generalisation of De Rham usual cohomology
Couverture souple
ISBN 10 : 3843364672 ISBN 13 : 9783843364676
Editeur : LAP LAMBERT Academic Publishing, 2010

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Biographie de l'auteur

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2010
Langue
anglais
ISBN 10 
3843364672
ISBN 13 
9783843364676
Reliure
Broché
Nombre de pages
84
Coordonnées du fabricant
non disponible
Personne responsable
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