A Study of Generalized Projective
P
−
Curvature Tensor on Warped Product Manifolds
Keyword(s):
The main aim of this study is to investigate the effects of the P − curvature flatness, P − divergence-free characteristic, and P − symmetry of a warped product manifold on its base and fiber (factor) manifolds. It is proved that the base and the fiber manifolds of the P − curvature flat warped manifold are Einstein manifold. Besides that, the forms of the P − curvature tensor on the base and the fiber manifolds are obtained. The warped product manifold with P − divergence-free characteristic is investigated, and amongst many results, it is proved that the factor manifolds are of constant scalar curvature. Finally, P − symmetric warped product manifold is considered.
2016 ◽
Vol 13
(07)
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pp. 1650099
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2019 ◽
Vol 11
(2)
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pp. 332-349
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2019 ◽
Vol 10
(3)
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pp. 193-202
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2002 ◽
Vol 30
(12)
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pp. 709-715
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2018 ◽
Vol 103
(117)
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pp. 69-75
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2015 ◽
Vol 145
(3)
◽
pp. 559-569
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