13 research outputs found
Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection
We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an η-Einstein manifold. We also investigate some properties of curvature tensor, conformal curvature tensor, W2-curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor with respect to canonical paracontact connection on a para-Sasakian manifold. It is shown that a concircularly flat para-Sasakian manifold with respect to canonical paracontact connection is of constant scalar curvature. We give some characterizations for pseudo-projectively flat para-Sasakian manifolds
η-Ricci solitons in (ε)-almost paracontact metric manifolds
The object of this paper is to study η -Ricci solitons on ( ε ) -almost paracontact metric manifolds. We investigate η -Ricci solitons in the case when its potential vector field is exactly the characteristic vector field ξ of the ( ε ) -almost paracontact metric manifold and when the potential vector field is torse-forming. We also study Einstein-like and ( ε )-para Sasakian manifolds admitting η-Ricci solitons. Finally we obtain some results for η -Ricci solitons on ( ε )-almost paracontact metric manifolds with a special view towards parallel symmetric (0,2) -tensor fields
Warped product submanifolds of Lorentzian paracosymplectic manifolds
In this paper we study the warped product submanifolds of a Lorentzian
paracosymplectic manifold and obtain some nonexistence results. We show that a
warped product semi-invariant submanifold in the form
{} of Lorentzian paracosymplectic manifold such that
the characteristic vector field is normal to is an usual Riemannian product
manifold where totally geodesic and totally umbilical submanifolds of warped
product are invariant and anti-invariant, respectively. We prove that the
distributions involved in the definition of a warped product semi-invariant
submanifold are always integrable. A necessary and sufficient condition for a
semi-invariant submanifold of a Lorentzian paracosymplectic manifold to be
warped product semi-invariant submanifold is obtained. We also investigate the
existence and nonexistence of warped product semi-slant and warped product
anti-slant submanifolds in a Lorentzian paracosymplectic manifold.Comment: This paper has been withdrawn by the autho