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

Abstract

Abstract. We introduce the notions of h-v-semi-slant submersions and almost h-v-semi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations, investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. We find a condition for such submersions to be totally geodesic. We also obtain an inequality of a h-v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and h-v-semi-slant angle. Finally, we give examples of such maps.

V-Quasi-Bi-Slant Riemannian Maps

“…Proof. The proof of Lemma 2 is the same as the one for v-semi-slant submersion (see Proposition (3.5) and Remark (3.6) of [22]). Hence we omit it.…”

“…Ref. [22]: Let π : (N 1 , g 1 , J) → (N 2 , g 2 ) be a Riemannian map. Then we say that π is a V-semi-slant Riemannian map if there is a distribution D 1 ⊂ (ker π * ) ⊥ such that:…”

“…In [22], Park introduced v-semi-slant submersions from almost Hermitian manifolds, and in [23], Sepet and Bozok proposed v-semi-slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. In this paper, we are interested in studying the above idea in the setting of v-QBSR maps.…”

Hemi-slant ξ⊥-Riemannian submersions in contact geometry

“…After this kind of submersions were studied between manifolds endowed with differentiable structures. Many authors studied different geometric properties of the Riemannian submersions, anti-invariant submersion [18,30,33], semi-invariant submersion [4,31], paraquaternionic 3-submersion [37], statistical submersion [38], slant submersion [11,12,15,27,32], semi-slant submersion [16,25,26], conformal slant submersion [2,17] , conformal semi-slant submersion [1], bi-slant submersion [34] and Quasi bi-slant submersion [28].…”