quasi-Sasakian Manifolds Research Articles

Differential geometry of quasi-Sasakian manifolds

The full system of structure equations of a quasi-Sasakian structure is obtained. The structure of the main tensors on a quasi-Sasakian manifold (the Riemann-Christoffel tensor, the Ricci tensor, and other tensors) is studied on this basis. Interesting characterizations of quasi-Sasakian Einstein manifolds are obtained. Additional symmetry properties of the Riemann-Christoffel tensor are discovered and used for distinguishing a new class of quasi-Sasakian manifolds. An exhaustive description of the local structure of manifolds in this class is given. A complete classification (up to the -transformation of the metric) is obtained for manifolds in this class having additional properties of the isotropy kind.

On cosymplectic quasi-Sasakian manifolds with quasi-Reeb vector field

On cosymplectic quasi-Sasakian manifolds with quasi-Reeb vector field

Normal contact CR-submanifolds of a quasi-Sasakian manifold

Normal contact CR-submanifolds of a quasi-Sasakian manifold

On three-dimensional conformally flat quasi-Sasakian manifolds

LetM be a 3-dimensional quasi-Sasakian manifold. On such a manifold, the so-called structure function β is defined. With the help of this function, we find necessary and sufficient conditions forM to be conformally flat. Next it is proved that ifM is additionally conformally flat with β = const., then (a)M is locally a product ofR and a 2-dimensional Kahlerian space of constant Gauss curvature (the cosymplectic case), or (b)M is of constant positive curvature (the non cosymplectic case; here the quasi-Sasakian structure is homothetic to a Sasakian structure). An example of a 3-dimensional quasi-Sasakian structure being conformally flat with nonconstant structure function is also described. For conformally flat quasi-Sasakian manifolds of higher dimensions see [O1]

Cosymplectic quasi-Sasakian pseudo-Riemannian manifolds and coisotropic foliations

Si considera una varieta neutra\(\tilde M\) di dimensione 2m munita di una struttura conforme simplettica\(CS_p \left( {2m; R} \right) = \left( {\tilde \Omega , \tilde \upsilon } \right)\). Vengono studiati i differenti problemi concernenti gli automorfismi infinitesimali della 2-forma quasi simplettica\(\tilde \Omega \). Inoltre vengono formulate alcune proprieta di un fogliettamento con isotropoF c su\(\tilde M\).

On quasi-Sasakian manifolds

On quasi-Sasakian manifolds

On Almost Contingent Manifolds of Second Class with Applications in Relativity

D. E. Blair [1] has introduced the notion of K-manifolds as an analogue of the even dimensional Kähler manifolds and of the odd dimensional quasi-Sasakian manifolds. These manifolds have been studied with respect to a positive definite metric. In this paper, we study a more general case of if-manifolds carrying an arbitrary non-degenerate metric, in particular, a metric of Lorentz signature. This theory is then applied within the frame-work of general relativity. Using the Ruse-Synge classification [8, 9] of non-null electromagnetic fields with source, we develop a geometric proof for the existence of either two space like or one space like and one time like Killing vector fields on the space-time manifold.

Quasi-Sasakian manifolds

Quasi-Sasakian manifolds