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The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, -projectively flat, -projectively flat, --projectively flat, pseudo projectively flat and -pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat,...
Fondements de la théorie des -produits. Notion de -produit de Vey; tout -produit est équivalent à un -produit de Vey. Sur toute variété symplectique paracompacte telle que , il existe des -produits de Vey. Caractérisation des algèbres de Lie engendrées par antisymétrisation d’un -produit (éventuellement faible); ce sont à une équivalence près, les algèbres de Lie de Vey.On considère les variétés symplectiques sur lesquelles opère, par symplectomorphismes, un groupe de Lie . Si admet...
We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of -metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among connections. We prove that the first canonical and the well adapted connections define a one-parameter family of adapted...
We define the divergence operators on a graded algebra, and we show that, given an odd
Poisson bracket on the algebra, the operator that maps an element to the divergence of
the hamiltonian derivation that it defines is a generator of the bracket. This is the
“odd laplacian”, , of Batalin-Vilkovisky quantization. We then study the
generators of odd Poisson brackets on supermanifolds, where divergences of graded vector
fields can be defined either in terms of berezinian volumes or of graded connections.
Examples...
For a double complex , we show that if it satisfies the -lemma and the spectral sequence induced by does not degenerate at , then it degenerates at . We apply this result to prove the degeneration at of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of -lemma.
Building on the theory of elliptic operators, we give a unified treatment of the
following topics: - the problem of homotopy invariance of Novikov’s higher
signatures on closed manifolds, - the problem of cut-and-paste invariance of
Novikov’s higher signatures on closed manifolds, - the problem of defining
higher signatures on manifolds with boundary and proving their homotopy invariance.
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