Admissible Hyper-Complex Pseudo-Hermitian Structures

Galaev, S. V.

doi:10.1134/s1995080218010122

Cited by 6 publications

(3 citation statements)

References 4 publications

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“…An almost contact metric manifold is called an almost contact Kähler manifold [5] if the following conditions hold:…”

Section: Sub-riemannian Manifolds Equipped With a Canonicalmentioning

confidence: 99%

“…By an almost quasi-Sasakian manifold (AQS-manifold) we mean an almost normal almost contact metric manifold with a closed fundamental form for which the condition dη( ξ, •) = 0 holds true. An almost contact metric manifold is called by the author of this paper almost normal if the equality Ñϕ = N ϕ + 2ϕ * dη ⊗ ξ = 0 holds [5]. The "almost normality" condition is equivalent to the integrability of the transversal structure.…”

Section: Introductionmentioning

confidence: 99%

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Almost quasi-Sasakian manifolds equipped with skew-symmetric connection

Galaev

2021

Preprint

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On a sub-Riemannian manifold, a connection with skew-symmetric torsion is defined as the unique connection from the class of N -connections that has this property. Two cases are considered separately: sub-Riemannian structure of even rank, and sub-Riemannian structure of odd rank. The resulting connection, called the canonical connection, is not a metric connection in the case when the sub-Riemannian structure is of even rank. The structure of an almost quasi-Sasakian manifold is defined as an almost contact metric structure of odd rank that satisfies additional requirements. Namely, it is required that the canonical connection is a metric connection and that the transversal structure is a Kähler structure. Both the quasi-Sasakian structure and the more general almost contact metric structure, called an almost quasi-Sasakian structure, satisfy these requirements. Sufficient conditions are found for an almost quasi-Sasakian manifold to be an Einstein manifold.

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“…An almost contact metric manifold is called an almost contact Kähler manifold [5] if the following conditions hold:…”

Section: Sub-riemannian Manifolds Equipped With a Canonicalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Almost quasi-Sasakian manifolds equipped with skew-symmetric connection

Galaev

2021

Preprint

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“…Естественность рассмотрения почти контактных метрических многообразий размерности n=4m+1, m≥1 с тремя структурными эндоморфизмами подтверждается результатами, опубликованными в работах[8][9][10]. В работе [11] рассматривается случай многообразия размерности n=4m+3.…”

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Geometry of Nonholonomic Kenmotsu Manifolds

Bukusheva¹

2021

Известия АлтГУ

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The concept of the intrinsic geometry of a nonholonomic Kenmotsu manifold M is introduced. It is understood as the set of those properties of the manifold that depend only on the framing of the D^ distribution D of the manifold M, on the parallel transformation of vectors belonging to the distribution D along curves tangent to this distribution. The invariants of the intrinsic geometry of the nonholonomic Kenmotsu manifold are: the Schouten curvature tensor; 1-form η generating the distribution D; the Lie derivative of the metric tensor g along the vector field ; Schouten — Wagner tensor field P, whose components in adapted coordinates are expressed using the equalities . It is proved that, as in the case of the Kenmotsu manifold, the Schouten — Wagner tensor of the manifold M vanishes. It follows that the Schouten tensor of a nonholonomic Kenmotsu manifold has the same formal properties as the Riemann curvature tensor. It is proved that the alternation of the Ricci — Schouten tensor coincides with the differential of the structural form. This property of the Ricci — Schouten tensor is used in the proof of the main result of the article: a nonholonomic Kenmotsu manifold cannot carry the structure of an η-Einstein manifold.

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$$\mathbf{3}$$-Kenmotsu Manifolds

Attarchi

2020

Lobachevskii J Math

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Admissible Hyper-Complex Pseudo-Hermitian Structures

Cited by 6 publications

References 4 publications

Almost quasi-Sasakian manifolds equipped with skew-symmetric connection

Almost quasi-Sasakian manifolds equipped with skew-symmetric connection

Geometry of Nonholonomic Kenmotsu Manifolds

$$\mathbf{3}$$-Kenmotsu Manifolds

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