Integral manifolds of the first fundamental distribution 𝑙𝑐𝐴𝐶𝑆-structure
https://doi.org/10.22405/2226-8383-2022-23-1-142-152
Abstract
In paper we consider aspects of the Hermitian geometry of 𝑙𝑐𝐴𝐶𝑆structures. The effect of the vanishing of the Neyenhuis tensor and the associated tensors 𝑁(1), 𝑁(2), 𝑁(3), 𝑁(4) on the class of almost Hermitian structure induced on the first fundamental distribution of 𝑙𝑐𝐴𝐶𝑆structures is investigated. It is proved that the almost Hermitian structure induced on integral manifolds of the first fundamental distribution: 𝑙𝑐𝐴𝐶𝑆-manifolds is a structure of the class 𝑊2 ⊕ 𝑊4,
and it will be almost K¨ahler if and only if 𝑔𝑟𝑎𝑑 𝜎 ⊂ 𝐿(𝜉); an integrable 𝑙𝑐𝐴𝐶𝑆-manifold is a structure of the class 𝑊4; a normal 𝑙𝑐𝐴𝐶𝑆-manifold is a K¨ahler structure; a 𝑙𝑐𝐴𝐶𝑆-manifold for which 𝑁(2)(𝑋, 𝑌 ) = 0, or 𝑁(3)(𝑋) = 0, or 𝑁(4)(𝑋) = 0, is an almost K¨ahler structure in the Gray-Herwell classification of almost Hermitian structures.
About the Authors
Aligaji Rustanov Rustanov
Institut of Digital Technologics and Modeling in Construction; National Research Moscow State University of Civil Engineering
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Elena Aleksandrovna Polkina
Institute of Physics, Technology and Informational Systems; Moscow State Pedagogical University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Galina Vasilyevna Teplyakova
Orenburg State University
Russian Federation
Russian Federation
candidate of pedagogical sciences
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Review
For citations:
Rustanov A.R., Polkina E.A., Teplyakova G.V. Integral manifolds of the first fundamental distribution 𝑙𝑐𝐴𝐶𝑆-structure. Chebyshevskii Sbornik. 2022;23(1):142-152. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-1-142-152
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