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zbMATH Open
Article . 2012
Data sources: zbMATH Open
Communications of the Korean Mathematical Society
Article . 2012 . Peer-reviewed
Data sources: Crossref
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LOCALLY SYMMETRIC HALF LIGHTLIKE SUBMANIFOLDS IN AN INDEFINITE KENMOTSU MANIFOLD

Locally symmetric half lightlike submanifolds in an indefinite Kenmotsu manifold
Authors: Jin, Dae Ho;

LOCALLY SYMMETRIC HALF LIGHTLIKE SUBMANIFOLDS IN AN INDEFINITE KENMOTSU MANIFOLD

Abstract

A codimension \(2\) submanifold \(M\) of a pseudo-Riemannian manifold \((\bar M, \bar g)\) is called half light-like if the radical distribution \(\mathrm{Rad}(TM)=TM \cap TM ^{\perp}\) is a vector subbundle of \(TM\) and \(TM^\perp\) has rank one. Because of possible ranks of \(\mathrm{Rad}(TM)\), all codimension \(2\) light-like submanifolds are either half light-like or coisotropic. Given a half light-like submanifold \(M\) of \((\bar M,\bar g)\), one has \[ T\bar M = TM \oplus \mathrm{tr}(TM)=\mathrm{Rad}(TM) \oplus \mathrm{tr}(TM)\oplus _{\mathrm{orth}} S(TM), \] where \(\mathrm{tr}(TM)\) and \( S(TM)\) respectively denote the transversal vector bundle and the screen distribution and \(\oplus _{\mathrm{orth}}\) denotes the \(\bar g\)-orthogonal direct sum. In the paper under review, the authors consider half light-like submanifolds of indefinite Kenmotsu manifolds \((\bar M, J,\zeta,\theta,\bar g)\). The following results are proved: \(\bullet\) The structure \(1\)-form \(\theta\) is closed on \(M\). \(\bullet\) If \(M\) is locally symmetric and \(tr(TM)\) is parallel (with respect to \(\bar \nabla\)), then the induced Ricci type tensor \(R^{(0,2)}\) of \(M\) is symmetric. \(\bullet\) If \(M\) is irrotational and locally symmetric and \(tr(TM)\) is parallel, then \(M\) has constant sectional curvature \(0\) and \(\zeta\) is normal to \(M\).

Keywords

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Special Riemannian manifolds (Einstein, Sasakian, etc.), irrotational submanifolds, Global submanifolds, local symmetry, half light-like submanifolds, indefinite Kenmotsu manifolds

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
bronze