Abstract
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 \({M=M_{\top}\times _{f}M_{\bot}}\) 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.
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The authors are very much thankful to the referees for their valuable suggestions.
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Yüksel Perktaş, S., Kılıç, E. & Keleş, S. Warped product submanifolds of Lorentzian paracosymplectic manifolds. Arab. J. Math. 1, 377–393 (2012). https://doi.org/10.1007/s40065-012-0037-y
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DOI: https://doi.org/10.1007/s40065-012-0037-y