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- W12194463 abstract "AbstractThe B-connection on almost complex manifolds with Norden metric is an ana-logue of the first canonical connection of Lihnerovich in Hermitian geometry. Inthe present paper it is considered a B-connection in the class of the quasi-Ka¨hlermanifold with Norden metric. Some necessary and sufficient conditions are derivedfor the corresponding curvature tensor to be Kahlerian. Curvature properties forthis connection are obtained. Conditions are given for the considered manifolds tobe isotropic-K¨ahler.Key words: almost complex manifold, Norden metric, nonintegrable structure,B-connection, quasi-Ka¨hler manifolds 2000 Mathematics Subject Classification: 53C15, 53C501. PreliminariesLet (M,J,g) be a 2n-dimensional almost complex manifold with Nordenmetric , i.e. M is a differentiable manifold with an almost complex structureJ and a metric g such that(1.1) J 2 x = −x, g(Jx,Jy) = −g(x,y)for arbitrary x, y of the algebra X(M) on the smooth vector fields on M.The associated metric ˜g of g on M is defined by ˜g(x,y) = g(x,Jy). Bothmetrics are necessarily of signature (n,n). The manifold (M,J,˜g) is an al-most complex manifold with Norden metric, too.Further, x, y, z, w will stand for arbitrary elements of X(M).A classification of the almost complex manifolds with Norden metric is givenin [1]. This classification is made with respect to the tensor field F of type(0,3) defined by(1.2) F(x,y,z) = g(∇" @default.
- W12194463 created "2016-06-24" @default.
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- W12194463 date "2008-04-25" @default.
- W12194463 modified "2023-09-27" @default.
- W12194463 title "ON THE GEOMETRY OF THE B-CONNECTION ON QUASI-K ¨ AHLER MANIFOLDS WITH NORDEN METRIC" @default.
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