On a Semi-symmetric Metric Connection in an Almost Kenmotsu Manifold with Nullity Distributions

Gopal Ghosh; Uday Chand De

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2016)

  • Volume: 55, Issue: 2, page 87-99
  • ISSN: 0231-9721

Abstract

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We consider a semisymmetric metric connection in an almost Kenmotsu manifold with its characteristic vector field ξ belonging to the ( k , μ ) ' -nullity distribution and ( k , μ ) -nullity distribution respectively. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric metric connection in an almost Kenmotsu manifold with ξ belonging to ( k , μ ) ' - and ( k , μ ) -nullity distribution respectively. Then we characterize an almost Kenmotsu manifold with ξ belonging to ( k , μ ) ' -nullity distribution admitting a semisymmetric metric connection.

How to cite

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Ghosh, Gopal, and De, Uday Chand. "On a Semi-symmetric Metric Connection in an Almost Kenmotsu Manifold with Nullity Distributions." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.2 (2016): 87-99. <http://eudml.org/doc/287900>.

@article{Ghosh2016,
abstract = {We consider a semisymmetric metric connection in an almost Kenmotsu manifold with its characteristic vector field $\xi $ belonging to the $(k,\mu )^\{\prime \}$-nullity distribution and $(k,\mu )$-nullity distribution respectively. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric metric connection in an almost Kenmotsu manifold with $\xi $ belonging to $(k,\mu )^\{\prime \}$- and $(k,\mu )$-nullity distribution respectively. Then we characterize an almost Kenmotsu manifold with $\xi $ belonging to $(k,\mu )^\{\prime \}$-nullity distribution admitting a semisymmetric metric connection.},
author = {Ghosh, Gopal, De, Uday Chand},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Semisymmetric metric connection; almost Kenmotsu manifold; Einstein manifold; sectional curvature; Ricci tensor; Weyl conformal curvature tensor},
language = {eng},
number = {2},
pages = {87-99},
publisher = {Palacký University Olomouc},
title = {On a Semi-symmetric Metric Connection in an Almost Kenmotsu Manifold with Nullity Distributions},
url = {http://eudml.org/doc/287900},
volume = {55},
year = {2016},
}

TY - JOUR
AU - Ghosh, Gopal
AU - De, Uday Chand
TI - On a Semi-symmetric Metric Connection in an Almost Kenmotsu Manifold with Nullity Distributions
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2016
PB - Palacký University Olomouc
VL - 55
IS - 2
SP - 87
EP - 99
AB - We consider a semisymmetric metric connection in an almost Kenmotsu manifold with its characteristic vector field $\xi $ belonging to the $(k,\mu )^{\prime }$-nullity distribution and $(k,\mu )$-nullity distribution respectively. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric metric connection in an almost Kenmotsu manifold with $\xi $ belonging to $(k,\mu )^{\prime }$- and $(k,\mu )$-nullity distribution respectively. Then we characterize an almost Kenmotsu manifold with $\xi $ belonging to $(k,\mu )^{\prime }$-nullity distribution admitting a semisymmetric metric connection.
LA - eng
KW - Semisymmetric metric connection; almost Kenmotsu manifold; Einstein manifold; sectional curvature; Ricci tensor; Weyl conformal curvature tensor
UR - http://eudml.org/doc/287900
ER -

References

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