Hemi-Slant Submersions

Abstract

As a generalization of anti-invariant submersions, semiinvariant submersions and slant submersions, we introduce the notion of hemi-slant submersion and study such submersions from Kählerian manifolds onto Riemannian manifolds. After we study the geometry of leaves of distributions which are involved in the definition of the submersion, we obtain new conditions for such submersions to be harmonic and totally geodesic. Moreover, we give a characterization theorem for the proper hemi-slant submersions with totally umbilical fibers.Mathematics Subject Classification. Primary 53C15, 53C43, 53B20.

Pointwise Bi-slant Submersions

“…A surjective ∞ -map : → is a ∞ -submersion if it has maximal rank at any point of . According to the conditions on the map , we have several types the following: Riemannian submersion [9,13], slant and semi-slant submersions [10,11,14,17], anti-invariant and semi-invariant Riemannian submersions [1,15,16], pointwise slant submersions [4,12], hemi-slant submersions [2,19], Lagrangian submersions [20], generic submersions [18] etc.…”

Hemi-slant ξ⊥-Riemannian submersions in contact geometry

“…As a generalization of anti-invariant, semi-invariant and slant submersion, Taştan et al defined the notion of hemi-slant Riemannian submersion in [36] (see also [3], [19], [24]).…”

Isotropic Riemannian submersions

“…Recently, B. Şahin [27] introduced the notion of anti-invariant Riemannian submersions which are Riemannian submersions from almost Hermitian manifolds such that the vertical distribution is anti-invariant under the almost complex structure of the total manifold. Later this notion has been extended for several cases, see: [1,2,4,8,9,16,19,20,23,26,29,30,32].…”