On Paraquaternionic Submersions Between Paraquaternionic Kähler Manifolds

Abstract

In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic submersions between paraquaternionic Kähler non locally hyper paraKähler manifolds. Then we examine, as an example, the canonical projection of the tangent bundle, endowed with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.2000 Mathematics Subject Classification 53C15, 53C26, 53C50.

Anti-Invariant Semi-Riemannian Submersions from Almost Para-Hermitian Manifolds

“…Since is a para-Kähler manifold, using (15) we get (∇ , ) = − ( , ∇ ) (18) for , ∈ Γ((ker * ) ⊥ ) and ∈ Γ(ker * ). Then using (6) we have (∇ , ) = − ( , ) − ( , V∇ ) . (19) Since V∇ ∈ Γ( ker * ), we obtain (16).…”

“…For instance, Riemannian submersions between almost contact manifolds were studied by Chinea in [4] under the name of almost contact submersions. Riemannian submersions have been also considered for quaternionic Kähler manifolds [5] and para-quaternionic Kähler manifolds [6,7]. This kind of submersions have been studied with different names by many authors (see [8][9][10][11][12][13][14], and more).…”

Slant submersions in paracontact geometry

“…Given a C ∞ −submersion ψ from a (semi)-Riemannian manifold (N, g N ) onto a (semi)-Riemannian manifold (B, g B ), according to the circumstances on the map ψ : (N, g N ) → (B, g B ), we get the following: a (semi)-Riemannian submersion ( [3,8,14,20]), an almost Hermitian submersion ( [27]), a paracontact submersion ( [9]), a paracontact paracomplex submersion ( [10]), a (para) quaternionic submersion ( [6,17]), a slant submersion ( [12,19,22,23]), an anti-invariant submersion ( [11,24]), a conformal semi-slant submersion ( [1,13]), a conformal anti-invariant submersion ( [2]), a hemi-slant submersion ( [25]), etc. As we know, Riemannian submersions were severally introduced by B. O'Neill ( [20]) and A.…”

Semi-invariant semi-Riemannian submersions

“…For instance, Riemannian submersions between almost contact manifolds were studied by Chinea in [5] under the name of almost contact submersions. Riemannian submersions have been also considered for quaternionic Kähler manifolds [14] and para-quaternionic Kähler manifolds [4], [15]. This kind of submersions have been studied with di¤erent names by many authors (see [1], [10], [12], [21], [22], [23], [24] and more).…”