Semi-Slant Submersions

Abstract

Abstract. We introduce semi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of slant submersions, semi-invariant submersions, anti-invariant submersions, etc. We obtain characterizations, investigate the integrability of distributions and the geometry of foliations, etc. We also find a condition for such submersions to be harmonic. Moreover, we give lots of examples.

Hemi-Slant Submersions

“…15 and 3.16 show that our conditions are different from the conditions found in[7]. From Theorems 3.15 and 3.16, we have also the following decomposition result.…”

“…There is an another generalization known as semi-slant submersion ( [7]) in the literature. However, we observe that there is no inclusion between the notion of semi-slant submersion and the notion of hemi-slant submersion in proper case.…”

“…He studied these type of submersions from a Kählerian manifold onto a Riemannian manifold. There are many other notions related to anti-invariant Riemannian submersion, such as Lagrangian submersion [12], semi-invariant submersion [9], slant submersion [10], pointwise slant submersion [5] and semi-slant submersion [7]. In particular, the notions of semi-invariant and slant submersion are natural generalizations of the notion of anti-invariant submersion whereas the notion of H. M. Taştan et al…”

H-v-Semi-Slant Submersions From Almost Quaternionic Hermitian Manifolds

“…and the angle θ = θ(X) between JX and the space (D 2 ) q is constant for nonzero X ∈ (D 2 ) q and q ∈ M , where D 2 is the orthogonal complement of D 1 in ker F * [21].…”

“…Given a C ∞ -submersion F from a (semi-)Riemannian manifold (M, g M ) onto a (semi-)Riemannian manifold (N, g N ), according to the conditions on the map F : (M, g M ) → (N, g N ), we can obtain the following: a semi-Riemannian submersion and a Lorentzian submersion [8], a Riemannian submersion ( [9], [16]), a slant submersion ( [6], [22]), an almost Hermitian submersion [24], a contact-complex submersion [10], a quaternionic submersion [11], an almost h-slant submersion [17], a semi-invariant submersion [23], an almost h-semiinvariant submersion [18], a semi-slant submersion [21], an almost h-semi-slant submersions [19], a v-semi-slant submersions [20], etc.…”