Semi-invariant ξ⊥-Riemannian submersions from almost contact metric manifolds

Abstract

As a generalization of anti-invariant [Formula: see text]-Riemannian submersions, we introduce semi-invariant [Formula: see text]-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We give examples, investigating the geometry of foliations which arise from the definition of a Riemannian submersion and proving a necessary and sufficient condition for a semi-invariant [Formula: see text]-Riemannian submersion to be totally geodesic. Moreover, we study semi-invariant [Formula: see text]-Riemannian submersions with totally umbilical fibers.

On quasi bi-slant Lorentzian submersions from LP -Sasakian manifolds

“…Recently, slant submersions, semi-invariant submersions as well as semi-slant submersions from almost Hermitian manifolds on Riemannian manifolds have been studied in [21,27,28], respectively. Several types of Riemannian submersions between Riemannian manifolds endowed with various constructures were investigated by several geometers ( [1,3,12,13,19,26,29]). In 2016, Sahin et al [31] proved decomposition theorems for hemi-slant Riemannian submersions from Hermitian manifolds on Riemannian manifolds.…”

Hemi-slant ξ⊥-Riemannian submersions in contact geometry

“…After this kind of submersions were studied between manifolds endowed with differentiable structures. Many authors studied different geometric properties of the Riemannian submersions, anti-invariant submersion [18,30,33], semi-invariant submersion [4,31], paraquaternionic 3-submersion [37], statistical submersion [38], slant submersion [11,12,15,27,32], semi-slant submersion [16,25,26], conformal slant submersion [2,17] , conformal semi-slant submersion [1], bi-slant submersion [34] and Quasi bi-slant submersion [28].…”

“…Recently, Akyol et al defined and studied of semi-invariant ξ ⊥ -Riemannian submersion and semi-slant ξ ⊥ -Riemannian submersion from almost contact manifolds onto Riemannian manifold [4,5,35]. They studied the geometry of this new submersions on almost contact manifolds.…”

Semi-invariant semi-Riemannian submersions

“…Riemannian submersions have been also considered for quaternionic Kähler manifolds [14] and para-quaternionic Kähler manifolds [4], [15]. This kind of submersions have been studied with di¤erent names by many authors (see [1], [10], [12], [21], [22], [23], [24] and more).…”