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$\mathcal{PSR}-$Submersions on Kaehler Manifolds and Casorati Inequalities along the Submersion
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In this paper, we offer a new submersion of a Kaehler manifold.This new class of submersion includes hemi-slant submersion,semi-slant submersion and bi-slant submersion as special classes. This partially slant Riemannian submersion, which we refer to briefly as $\boldsymbol{\mathcal{PSR}}-$submersion from Kaehler manifoldsto Riemannian manifolds, will be presented through through both trivial and non-trivial examples and characterizations. We also investigate the integrability and totally geodesic nature of the distributions and the $J-$pluriharmonicity ofsuch submersion. Finally, we investigate several curvature relations in complex space forms, involving Casorati curvatures for $\boldsymbol{\mathcal{PSR}}-$submersion.
Title: $\mathcal{PSR}-$Submersions on Kaehler Manifolds and Casorati Inequalities along the Submersion
Description:
In this paper, we offer a new submersion of a Kaehler manifold.
This new class of submersion includes hemi-slant submersion,semi-slant submersion and bi-slant submersion as special classes.
This partially slant Riemannian submersion, which we refer to briefly as $\boldsymbol{\mathcal{PSR}}-$submersion from Kaehler manifoldsto Riemannian manifolds, will be presented through through both trivial and non-trivial examples and characterizations.
We also investigate the integrability and totally geodesic nature of the distributions and the $J-$pluriharmonicity ofsuch submersion.
Finally, we investigate several curvature relations in complex space forms, involving Casorati curvatures for $\boldsymbol{\mathcal{PSR}}-$submersion.
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