Hemi-slant ξ⊥-Riemannian submersions in contact geometry

Abstract

M. A. Akyol and R. Sar? [On semi-slant ??-Riemannian submersions, Mediterr. J. Math. 14(6) (2017) 234.] defined semi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. As a generalization of the above notion and natural generalization of anti-invariant ??-Riemannian submersions, semi-invariant ??-Riemannian submersions and slant submersions, we study hemi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We obtain the geometry of foliations, give some examples and find necessary and sufficient condition for the base manifold to be a locally product manifold. Moreover, we obtain some curvature relations from Sasakian space forms between the total space, the base space and the fibres.

Quasi hemi-slant pseudo-Riemannian submersions in para-complex geometry

“…A C ∞ −submersion ψ can be defined according to the following conditions. A pseudo-Riemannian submersion ( [12], [16], [13], [17], [26]), an almost Hermitian submersion ( [27], [29]), bi-slant submanifold ( [3], [5]), a slant submersion ( [7], [11], [1], [19], [23]), bi-slant submersion ( [21]), an anti-invariant submersion ( [8], [9], [10], [24]), a hemi-slant submersion ( [28], [22]), a quasi-bi-slant Submersion ( [20]), a semi-invariant submersion ( [18], [25]), etc. As we know, Riemannian submersions were severally introduced by B. O'Neill ( [17]) and A.…”

Generic Submersions in Contact Geometry

“…Besides this, Watson considered the Riemannian submersions in a complex context and defined and studied so-called almost Hermitian submersions [3]. Later, the theory of submersion became a popular field, and it has also been worked in the contact context [4,5]. Most recent submersion studies can be found in the books [6,7].…”

Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry

“…A C ∞ −submersion ψ can be defined according to the following conditions. A pseudo-Riemannian submersion ( [4], [15], [21], [22], [34]), an almost Hermitian submersion ( [37], [32], [10]), a slant submersion ( [19], [9], [25], [31]), a para quaternionic submersion ( [5], [16] ), a Clairaut Submersion ( [12]), an anti-invariant submersion ( [11], [13], [30], [8]), anti-invariant Riemnnian submersion from cosymplectic manifolds ( [30], [14]), a quasi-bi-slant Submersion ( [27]), a pointwise slant submersion( [20], [28]), a hemi-slant submersion ( [35], [29]), a semi-invariant submersion ( [23], [33]), a semi-slant ξ ⊥ -Riemannian submersions ( [1], [26]), etc. As we know, Riemannian submersions were severally introduced by B. O'Neill ( [22]) and A.…”