Lagrangian submersions from normal almost contact manifolds

Taştan, Hakan Mete

doi:10.2298/fil1712885t

Cited by 14 publications

(11 citation statements)

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“…Definition 4.3. [34] Let γ be an anti-invariant Lorentzian submersion from an (LCS) n -manifold (L, φ, ζ, η, g, α) onto a semi-Riemannian manifold (S, g N ).…”

Section: Anti-invariant Lorentzian and Lagrangian Lorentzian Submersi...mentioning

confidence: 99%

“…Since then, the topics of anti-invariant Riemannian submersions and Lagrangian submersions have become an active field for researchers. The extension of anti-invariant Riemannian submersion as various types of submersions, such as antiinvariant ξ ⊥ -Riemannian submersions and Lagrangian submersions, have been studied in different forms of structures such as Kähler [28,29], nearly Kähler [22], almost product [30], locally product Riemannian [31], Sasakian [32][33][34], Kenmotsu [35], cosymplectic [36] and hyperbolic structures [37,38]. Moreover, a Lagrangian submersion is a specific version of anti-invariant Riemannian submersion such that the total manifold (almost complex structure) interchanges the role of horizontal and vertical distributions [39].…”

Section: Introductionmentioning

confidence: 99%

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Anti-Invariant Lorentzian Submersions From Lorentzian Concircular Structure Manifolds

et al. 2022

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This research article attempts to investigate anti-invariant Lorentzian submersions and the Lagrangian Lorentzian submersions (LLS) from the Lorentzian concircular structure [in short (LCS)n] manifolds onto semi-Riemannian manifolds with relevant non-trivial examples. It is shown that the horizontal distributions of such submersions are not integrable and their fibers are not totally geodesic. As a result, they can not be totally geodesic maps. Anti-invariant and Lagrangian submersions are also explored for their harmonicity. We illustrate that if the Reeb vector field is horizontal, the anti-invariant and LLS can not be harmonic.

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“…Definition 4.3. [34] Let γ be an anti-invariant Lorentzian submersion from an (LCS) n -manifold (L, φ, ζ, η, g, α) onto a semi-Riemannian manifold (S, g N ).…”

Section: Anti-invariant Lorentzian and Lagrangian Lorentzian Submersi...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Anti-Invariant Lorentzian Submersions From Lorentzian Concircular Structure Manifolds

et al. 2022

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“…Definition 4.3. ( [12] ) Let ψ be the anti-invariant Riemannian submersion from the almost contact metric manifold (M, w, ξ, η, g) on the Riemannian manifold (N, g N ). In case μ 5 {0} or μ 5 span{ξ}, i.e.…”

Section: Ajmsmentioning

confidence: 99%

Clairaut anti-invariant submersions from Lorentzian trans-Sasakian manifolds

Siddiqi

Chaubey²,

Siddiqui

2021

AJMS

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PurposeThe central idea of this research article is to examine the characteristics of Clairaut submersions from Lorentzian trans-Sasakian manifolds of type (α, β) and also, to enhance this geometrical analysis with some specific cases, namely Clairaut submersion from Lorentzian α-Sasakian manifold, Lorentzian β-Kenmotsu manifold and Lorentzian cosymplectic manifold. Furthermore, the authors discuss some results about Clairaut Lagrangian submersions whose total space is a Lorentzian trans-Sasakian manifolds of type (α, β). Finally, the authors furnished some examples based on this study.Design/methodology/approachThis research discourse based on classifications of submersion, mainly Clairaut submersions, whose total manifolds is Lorentzian trans-Sasakian manifolds and its all classes like Lorentzian Sasakian, Lorenztian Kenmotsu and Lorentzian cosymplectic manifolds. In addition, the authors have explored some axioms of Clairaut Lorentzian submersions and illustrates our findings with some non-trivial examples.FindingsThe major finding of this study is to exhibit a necessary and sufficient condition for a submersions to be a Clairaut submersions and also find a condition for Clairaut Lagrangian submersions from Lorentzian trans-Sasakian manifolds.Originality/valueThe results and examples of the present manuscript are original. In addition, more general results with fair value and supportive examples are provided.

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“…A surjective ∞ -map : → is a ∞ -submersion if it has maximal rank at any point of . According to the conditions on the map , we have several types the following: Riemannian submersion [9,13], slant and semi-slant submersions [10,11,14,17], anti-invariant and semi-invariant Riemannian submersions [1,15,16], pointwise slant submersions [4,12], hemi-slant submersions [2,19], Lagrangian submersions [20], generic submersions [18] etc.…”

Section: Given Andmentioning

confidence: 99%

Pointwise Bi-slant Submersions

Sepet

2020

Celal Bayar Üniversitesi Fen Bilimleri Dergisi

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In the present paper we study pointwise bi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of anti-invariant, semi-invariant, slant, bi-slant, pointwise semislant, pointwise slant, pointwise hemi-slant submersions. We mainly focus on pointwise bi-slant submersions from Kaehler manifolds onto Riemannian manifolds. We give some characterizations for such maps. We obtain necessary and sufficient conditions for the totally geodesicness of the distributions 1 and 2 mentioned in the definition of the pointwise bi-slant submersions. Also we investigate the geometry of vertical and horizontal distributions. Then we give necessary and sufficient conditions for pointwise bi-slant submersions to be totally geodesic.

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Lagrangian submersions from normal almost contact manifolds

Cited by 14 publications

References 0 publications

Anti-Invariant Lorentzian Submersions From Lorentzian Concircular Structure Manifolds

Anti-Invariant Lorentzian Submersions From Lorentzian Concircular Structure Manifolds

Clairaut anti-invariant submersions from Lorentzian trans-Sasakian manifolds

Pointwise Bi-slant Submersions

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