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 Chebyshevskii Sb., 2017, Volume 18, Issue 2, Pages 183–194 (Mi cheb550)

The structure of almost Hermitian structures of total space of principal fiber $T^1$-bundle with flat connection over some classes of almost contact metric manifolds

I. A. Petrov

Moscow

Abstract: In paper we studied almost Hermitian structures of total space of principal fiber $T^1$-bundle with flat connection over some classes of almost contact metric manifolds, such as contact, $K$-contact, Sasakian, normal, cosymplectic, nearly cosymplectic, exactly cosymplectic and weakly cosymplectic manifolds. Over contact and $K$-contact manifolds almost Hermitian structure belongs to the $W_2 \oplus W_4$ class. Lee's form is different from the form of the flat connection by constant factor, equal to $-2$. Moreover, dual Lee's vector field is different from some vector field from vertical distribution by the same constant factor. Also, this almost Hermitian structure is local conformal almost Kahlerian. Over Sasakian manifolds almost Hermitian structure belongs to the $W_4$ class. Lee's form is different from the form of the flat connection by constant factor, equal to $2$. Moreover, dual Lee's vector field also is different from some vector field from vertical distribution by the same constant factor. Over weakly cosymplectic manifolds almost Hermitian structure is semiKahlerian. Lee's form and dual Lee's vector field are identically zero. Over cosymplectic manifolds almost Hermitian structure is Kahlerian. Also, Lee's form and dual Lee's vector field are identically zero. Over normal manifolds almost Hermitian structure is Hermitian. Over exactly cosymplectic manifolds almost Hermitian structure is $G_1$ almost Hermitian structure, and over nearly cosymplectic manifolds almost Hermitian structure is $G_2$ almost Hermitian structure.
Bibliography: 15 titles.

Keywords: principal fiber $T^1$-bundle, almost contact metric structure, almost Hermitian structure, Lee's form, local conformity.

DOI: https://doi.org/10.22405/2226-8383-2017-18-2-183-194

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Bibliographic databases:

UDC: 514.76
Accepted:14.06.2017

Citation: I. A. Petrov, “The structure of almost Hermitian structures of total space of principal fiber $T^1$-bundle with flat connection over some classes of almost contact metric manifolds”, Chebyshevskii Sb., 18:2 (2017), 183–194

Citation in format AMSBIB
\Bibitem{Pet17} \by I.~A.~Petrov \paper The structure of almost Hermitian structures of total space of principal fiber $T^1$-bundle with flat connection over some classes of almost contact metric manifolds \jour Chebyshevskii Sb. \yr 2017 \vol 18 \issue 2 \pages 183--194 \mathnet{http://mi.mathnet.ru/cheb550} \crossref{https://doi.org/10.22405/2226-8383-2017-18-2-183-194} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3668962} \elib{https://elibrary.ru/item.asp?id=30042548}