|
Integral manifolds of the first fundamental distribution $lcAC_S$-structure
A. R. Rustanova, E. A. Polkinab, G. V. Teplyakovac a Institut of Digital Technologics and Modeling in Construction, National Research Moscow State University of Civil Engineering (Moscow)
b Institute of Physics, Technology and Informational Systems, Moscow State Pedagogical University (Moscow)
c Orenburg State University (Orenburg)
Abstract:
In paper we consider aspects of the Hermitian geometry of $lcAC_S$structures. 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 $lcAC_S$structures is investigated. It is proved that the almost Hermitian structure induced on integral manifolds of the first fundamental distribution: $lcAC_S $-manifolds is a structure of the class $W_2\oplus W_4$, and it will be almost Kähler if and only if $grad \ \sigma \subset L(\xi)$; an integrable $lcAC_S $-manifold is a structure of the class $W_4$; a normal $lcAC_S$-manifold is a Kähler structure; a $lcAC_S $-manifold for which $N^{(2)} (X,Y)=0$, or $N^{(3)} (X)=0$, or $N^{(4)} (X)=0$, is an almost Kähler structure in the Gray-Herwell classification of almost Hermitian structures.
Keywords:
almost contact structures, almost Hermitian structures, integrability of structures, Neyenhuis tensor, normal structures.
Received: 04.08.2021 Accepted: 27.02.2022
Citation:
A. R. Rustanov, E. A. Polkina, G. V. Teplyakova, “Integral manifolds of the first fundamental distribution $lcAC_S$-structure”, Chebyshevskii Sb., 23:1 (2022), 142–152
Linking options:
https://www.mathnet.ru/eng/cheb1160 https://www.mathnet.ru/eng/cheb/v23/i1/p142
|
Statistics & downloads: |
Abstract page: | 29 | Full-text PDF : | 6 | References: | 8 |
|