From symplectic and contact geometry to dynamical systems
The Lichnerowicz cohomology as an intersting generalisation of De Rham usual cohomology
Versandkostenfrei!
Versandfertig in 6-10 Tagen
32,99 €
inkl. MwSt.
PAYBACK Punkte
16 °P sammeln!
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 n...
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.
Andere Kunden interessierten sich für
