On semi-slant $ξ^\perp-$Riemannian submersions
On semi-slant $ξ^\perp-$Riemannian submersions
The aim of the present paper to define and study semi-slant $ξ^\perp-$Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of anti-invariant $ξ^\perp-$Riemannian submersions, semi-invariant $ξ^\perp-$Riemannian submersions and slant Riemannian submersions. We obtain characterizations, investigate the geometry of foliations which arise from the definition of this new submersion. After we investigate the geometry of foliations, we obtain necessary and sufficient condition for base manifold to be a locally product manifold and proving new conditions to be totally umbilical and totally geodesicness, respectively. Moreover, some examples of such submersions are mentioned.
15 pages
Mathematics - Differential Geometry, Local submanifolds, Differential Geometry (math.DG), 53C15, 53C40, Foliations (differential geometric aspects), General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Riemannian submersion, anti-invariant \(\xi^\perp \)-Riemannian submersion, slant Riemannian submersion, semi-invariant \(\xi^\perp \)-Riemannian submersion, Sasakian manifold
Mathematics - Differential Geometry, Local submanifolds, Differential Geometry (math.DG), 53C15, 53C40, Foliations (differential geometric aspects), General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Riemannian submersion, anti-invariant \(\xi^\perp \)-Riemannian submersion, slant Riemannian submersion, semi-invariant \(\xi^\perp \)-Riemannian submersion, Sasakian manifold
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