We define the notions of strong and strict recurrency for actions countable ordered groups on σ-finite non atomic measure spaces with quasi-invariant measures. show that is equivalent to existence weakly wandering sets positive measure. also certain p.m.p ergodic system not strictly recurrent, which shows are equivalent.

The Casimir forces on two parallel plates moving by uniform proper acceleration in static de Sitter background due to conformally coupled massless scalar field satisfying Dirichlet boundary conditions on the plates is investigated. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally inv...

The energy-momentum tensor for a massless conformally coupled scalar field in de Sitter spacetime in the presence of a couple curved branes is investigated. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for co...

The problem of characterizing conformally Einstein manifolds by tensorial conditions has been tackled recently in papers by M. Listing, and in work by A. R. Gover and P. Nurowski. Their results apply to metrics satisfying a " non-degeneracy " condition on the Weyl tensor W. We investigate the geometry of the foliations arising on conformally Einstein spaces (with Riemannian signature) where thi...

An algebraic curvature tensor is called Osserman if the eigenvalues of the associated Jacobi operator are constant on the unit sphere. A Riemannian manifold is called conformally Osserman if its Weyl conformal curvature tensor at every point is Osserman. We prove that a conformally Osserman manifold of dimension n 6= 3, 4, 16 is locally conformally equivalent either to a Euclidean space or to a...

We study a 1-form which can be given by a vector in a conformally invariant way. We then study conformally invariant functionals associated to a “Y-diagram” on the space of knots which are made from the 1-form.

The object of the present paper is to study quasi-conformally flat generalized Sasakian-space-forms. Also we study quasi-conformally semisymmetric generalized Sasakian-space-forms. As a consequence of the results, we obtain some important corollaries.