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

Attarchi, Hassan

doi:10.1134/s1995080220030051

Cited by 1 publication

(3 citation statements)

References 16 publications

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“…где Г(D) -модуль допустимых векторных полей (векторных полей, в каждой точке принадлежащих распределению D). Внутренняя связность определяет дифференцирование допустимых тензорных полей [7]. Вот так, например, определяется ковариантная производная эндоморфизма…”

Section: Av Bukushevaunclassified

“…-тензор Схоутена -Риччи [7]. В адаптированных координатах получаем: Левая часть последнего равенства зависит от координаты x n , а правая -нет, что и доказывает теорему.…”

Section: Av Bukushevaunclassified

“…Заметим, что в отличие от классического случая многообразия Кенмоцу тензор Схоутена неголономного многообразия Кенмоцу в нуль не обращается. Это утверждение следует из известной формулы [7]:…”

Section: Av Bukushevaunclassified

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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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Section: Av Bukushevaunclassified

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Geometry of Nonholonomic Kenmotsu Manifolds

Bukusheva¹

2021

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

Cited by 1 publication

References 16 publications

Geometry of Nonholonomic Kenmotsu Manifolds

Geometry of Nonholonomic Kenmotsu Manifolds

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