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On almost cosymplectic (κ,μ,ν)-spaces

Piotr Dacko, Zbigniew Olszak (2005)

Banach Center Publications

An almost cosymplectic (κ,μ,ν)-space is by definition an almost cosymplectic manifold whose structure tensor fields φ, ξ, η, g satisfy a certain special curvature condition (see formula (eq1b)). This condition is invariant with respect to the so-called -homothetic transformations of almost cosymplectic structures. For such manifolds, the tensor fields φ, h ( = ( 1 / 2 ) ξ φ ), A ( = -∇ξ) fulfill a certain system of differential equations. It is proved that the leaves of the canonical foliation of an almost cosymplectic...

On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity

Uday Chand De, Avik De (2012)

Czechoslovak Mathematical Journal

The object of the present paper is to study almost pseudo-conformally symmetric Ricci-recurrent manifolds. The existence of almost pseudo-conformally symmetric Ricci-recurrent manifolds has been proved by an explicit example. Some geometric properties have been studied. Among others we prove that in such a manifold the vector field ρ corresponding to the 1-form of recurrence is irrotational and the integral curves of the vector field ρ are geodesic. We also study some global properties of such a...

On canonical screen for lightlike submanifolds of codimension two

K. Duggal (2007)

Open Mathematics

In this paper we study two classes of lightlike submanifolds of codimension two of semi-Riemannian manifolds, according as their radical subspaces are 1-dimensional or 2-dimensional. For a large variety of both these classes, we prove the existence of integrable canonical screen distributions subject to some reasonable geometric conditions and support the results through examples.

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