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 a Lorentzian paracosymplectic manifold such that the characteristic vector field is normal to...

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Bibliographic Details
Published in:Arabian journal of mathematics 2012-09, Vol.1 (3), p.377-393
Main Authors: Yüksel Perktaş, Selcen, Kılıç, Erol, Keleş, Sadık
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Research Article
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Summary: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 a Lorentzian paracosymplectic manifold such that the characteristic vector field is normal to M is a 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.
ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-012-0037-y