{"product_id":"from-symplectic-and-contact-geometry-to-dynamical-systems-von-hassan-ait-haddou","title":"From symplectic and contact geometry to dynamical systems","description":"\u003cp\u003eIn 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783843364676\"\u003e\u003ch3\u003eThe Lichnerowicz cohomology as an intersting generalisation of De Rham usual cohomology\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783843364676","offer_id":39470078230621,"sku":"9783843364676","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/f1d42a40-170c-4197-bb97-d860ed3fc5a8.jpg?v=1758778659","url":"https:\/\/shop.autorenwelt.de\/products\/from-symplectic-and-contact-geometry-to-dynamical-systems-von-hassan-ait-haddou","provider":"Autorenwelt Shop","version":"1.0","type":"link"}