H-Slant Submersions

Abstract

Abstract. In this paper, we define the almost h-slant submersion and the h-slant submersion which may be the extended version of the slant submersion [11]. And then we obtain some theorems which come from the slant submersion's cases. Finally, we construct some examples for the almost h-slant submersions and the h-slant submersions. . The paper is organized as follows. In Section 2 we recall some notions needed for this paper. In Section 3 we give the definitions of the almost h-slant submersion and the h-slant submersion and obtain some interesting properties about them. In Section 4 we construct some examples for the almost h-slant submersions and the h-slant submersions. Introduction PreliminariesLet (M, E, g) be an almost quaternionic Hermitian manifold, where M is a 4n-dimensional differentiable manifold, g is a Riemannian metric on M , and E is a rank 3 subbundle of End(T M ) such that for any point p ∈ M with its some neighborhood U , there exists a local basis {J 1 , J 2 , J 3 } of sections of E on U satisfying for all α ∈ {1, 2, 3}

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

“…is said to be an almost h-slant submersion if given a point p ∈ M with a neighborhood U , there exists a quaternionic Hermitian basis {I, J, K} of sections of E on U such that for R ∈ {I, J, K} the angle θ R = θ R (X) between RX and the space ker(F * ) q is constant for nonzero X ∈ ker(F * ) q and q ∈ U [17].…”

“…J, K}, then we call the map F an almost h-v-slant submersion and the angles {θ I , θ J , θ K } almost h-v-slant angles [17]. Otherwise, if θ R = π 2 for R ∈ {I, J, K}, then we call the map F an almost h-v-semi-invariant submersion [18].…”

“…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.…”

Semi-Slant Submersions from Almost Product Riemannian Manifolds

“…Riemannian submersion ( [5], [11]), slant submersion ( [6], [12], [13]), almost Hermitian submersion [16], quaternionic submersion [7], etc. As we know, Riemannian submersions are related with physics and have their applications in the Yang-Mills theory ( [3], [17]), Kaluza-Klein theory ( [2], [8]), semi-invariant submersion( [14]), supergravity and superstring theories ( [9], [10]), etc.…”

“…From (5), (6), (12) and (13) we get p∇π˚qpX, Y q "´π˚pφ∇ X φY`ω∇ X φY`BT X φY`CT X φỲ φT X ωY`ωT X ωY`Bh∇ X ωY`Ch∇ X ωY q.…”