On Quasi-Hemi-Slant Riemannian Submersion

Abstract

We recall the notions of invariant, anti-invarian, semi-invariant, slant, semi-slant, quasi-slant and hemi-slant Riemannian submersions from almost Hermitian manifolds to a Riemannian manifolds. In this paper we contruct a Riemannian submersion which generalizes hemi-slant, semi-slant and semi-invariant Riemanian submersions from almost Hermitian manifold to a Riemannian manifold and study its geometry.

On Quasi-Hemi-Slant Riemannian Maps

“…If Ker F * = D  D1 D2, J (D) = D, JD2  (ker F * ) ⊥ the angle  between JZ and the space (D1)p is constant for any non-zero vector Z in (D1)p then F is said to be quasi-hemi-slant Riemannian map and the angle  is said to be the quasi-hemi-slant angle of the map [17].…”

“…Sayar, Akyol and Prasad studied on bi slant submersions [15], and Prasad, Shukla and Kumar introduce quasi-bi slant submersions [16]. Recently, Longwap, Massamba and Homti introduce and study quasi-hemi slant Riemannian submersions which generalizes hemi-slant, semi-slant and semi-invariant Riemannian submersions [17]. It is well known that Riemannian submersion is a particular Riemannian map with (range F * ) ⊥ = {0}, so we generalize the notion of quasihemi slant Riemannian submersions to quasi-hemi slant Riemannian maps in the present paper and study its geometry.…”

Local Orthonormal Basis of the Fibres of Quasi-Hemi-Slant Riemannian Submersion

“…Many other Geometers have introduced several other kinds of submersions base on conditions associated with the submersion. Some of these well known submersions are; Invariant submersion [5], Semi-Invarian submersion [6], Anti-invariant Submersion [7], Submersion of Semi-Invarian Submanifolds of Trans-Sasakian Manifold [8], Geometry of slant Submanifolds [9], slant submersion from Almost Hermitian manifold [10], Semi-Slant submersion [11], quaternionic submersion [12], Riemannian Submersion from Almost contact metric manifolds [13], almost h-slant submersion and h-slant submersion [14], Hemi-Slant submersion [15] and the one introduced; Quasi-Hemi-Slant Riemannian Submersion [16].…”

Conformal Quasi-Hemi-Slant Riemannian Maps

“…Particularly, the concept of Riemannian submersions [7] and isometric immersions [6] were studied by Falcitelli and Chen. Then, Riemannian submersions were studied in various types as an anti-invariant, a semi-invariant, a slant, a hemi-slant, etc [13,25]. Submersions between almost Hermitian manifolds expanded to almost Hermitian submersions [30].…”