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Warped product submanifolds of Lorentzian paracosymplectic manifolds
- Publication Year :
- 2011
- Publisher :
- arXiv, 2011.
-
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 {$M=M_{T}\times_{f}M_{\bot}$} of Lorentzian paracosymplectic manifold such that the characteristic vector field is normal to $M$ 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.<br />Comment: This paper has been withdrawn by the author
- Subjects :
- Mathematics - Differential Geometry
Pure mathematics
Integrable system
General Mathematics
Mathematical analysis
Field (mathematics)
Submanifold
Manifold
53C15, 53B25, 53C40
Differential Geometry (math.DG)
Computer Science::Sound
Product (mathematics)
FOS: Mathematics
Mathematics::Differential Geometry
Invariant (mathematics)
Warped geometry
Mathematics::Symplectic Geometry
Eigenvalues and eigenvectors
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....4274cd075e7896b6a9a2e125ffc2f486
- Full Text :
- https://doi.org/10.48550/arxiv.1103.0687