On Slant Riemannian Submersions for Cosymplectic Manifolds

Erken, İrem Küpeli; Murathan, Cengizhan

doi:10.4134/bkms.2014.51.6.1749

Cited by 30 publications

(8 citation statements)

References 22 publications

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“…Proof. The proof is similar to the proof of Theorem 2 of [10], so we omit it.…”

Section: Pointwise Bi-slant Submersionsmentioning

confidence: 99%

Pointwise bi-slant submersions from cosymplectic manifolds

Sepet¹,

Ergüt²

2020

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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We introduce pointwise bi-slant submersions from cosymplectic manifolds onto Riemannian manifolds as a generalization of anti-invariant, semi-invariant, semi-slant, hemi-slant, pointwise semi-slant, pointwise hemislant and pointwise slant Riemannian submersions. We give an example for pointwise bi-slant submersions and investigate integrability and totally geodesicness of the distributions which are mentioned in the de…nition of pointwise bi-slant submersions admitting vertical Reeb vector …eld. Also we obtain necessary and su¢ cient conditions for such submersions to be totally geodesic maps.

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“…Proof. The proof is similar to the proof of Theorem 2 of [10], so we omit it.…”

Section: Pointwise Bi-slant Submersionsmentioning

confidence: 99%

Pointwise bi-slant submersions from cosymplectic manifolds

Sepet¹,

Ergüt²

2020

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…Thus, the map ψ 3 is a conformal slant submersion with the slant angle ω = π 4 and dilation λ = e 11 . Suppose that ψ 3 : N → B is a slant submersion [18]. Then the map ψ 3 is a conformal slant submersion with dilation λ = 1.…”

Section: Conformal Slant Submersionsmentioning

confidence: 99%

Conformal slant submersions from cosymplectic manifolds

Gündüzalp¹,

Akyol²

2018

Turk J Math

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Akyol [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistics 2017; 462: 177-192] defined and studied conformal antiinvariant submersions from cosymplectic manifolds.The aim of the present paper is to define and study the notion of conformal slant submersions (it means the Reeb vector field ξ is a vertical vector field) from cosymplectic manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions, and conformal antiinvariant submersions. More precisely, we mention many examples and obtain the geometries of the leaves of vertical distribution and horizontal distribution, including the integrability of the distributions, the geometry of foliations, some conditions related to total geodesicness, and harmonicity of the submersions. Finally, we consider a decomposition theorem on the total space of the new submersion.

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“…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.…”

Section: Introductionmentioning

confidence: 99%