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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 3

Horizontally submersions of contact CR-submanifolds

Fortuné MASSAMBA
Tshikunguila TSHIKUNA-MATAMBA
Pages
436–453
Publication Date
2014-05-16
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We finally prove that, under a certain condition, the contact CR-submanifold of a quasi Kenmotsu manifold is locally a product of a totally geodesic leaf of an integrable horizontal distribution and a curve tangent to the normal distribution.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we discuss some geometric properties of almost contact metric submersions involving symplectic manifolds.
📊
Key Findings & Data:We show that the structures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds are related to (1, 2)-symplectic structures.
💡
Conclusion & Impact:We finally prove that, under a certain condition, the contact CR-submanifold of a quasi Kenmotsu manifold is locally a product of a totally geodesic leaf of an integrable horizontal distribution and a curve tangent to the normal distribution.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:CR-submanifold · almost Hermitian manifold · almost contact metric submersion

Abstract

In this paper, we discuss some geometric properties of almost contact metric submersions involving symplectic manifolds. We show that the structures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds are related to (1, 2)-symplectic structures. For horizontally submersions of contact CR-submanifolds of quasi-K-cosymplectic and quasi-Kenmotsu manifolds, we study the principal characteristics and prove that their total spaces are CR-product. Curvature properties between curvatures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds and the base spaces of such submersions are also established. We finally prove that, under a certain condition, the contact CR-submanifold of a quasi Kenmotsu manifold is locally a product of a totally geodesic leaf of an integrable horizontal distribution and a curve tangent to the normal distribution.

Özet

In this paper, we discuss some geometric properties of almost contact metric submersions involving symplectic manifolds. We show that the structures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds are related to (1, 2)-symplectic structures. For horizontally submersions of contact CR-submanifolds of quasi-K-cosymplectic and quasi-Kenmotsu manifolds, we study the principal characteristics and prove that their total spaces are CR-product. Curvature properties between curvatures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds and the base spaces of such submersions are also established. We finally prove that, under a certain condition, the contact CR-submanifold of a quasi Kenmotsu manifold is locally a product of a totally geodesic leaf of an integrable horizontal distribution and a curve tangent to the normal distribution.

🔖

Cite This Article

MASSAMBA, F., TSHIKUNA-MATAMBA, T. (2014). Horizontally submersions of contact CR-submanifolds. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 3, 436–453. https://ajindex.com/articles/185706

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References (8)

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