Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. Saratov Univ. Math. Mech. Inform.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, Volume 15, Issue 2, Pages 136–141
DOI: https://doi.org/10.18500/1816-9791-2015-15-2-136-141
(Mi isu574)
 

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Almost contact metric structures defined by a symplectic structure over a distribution

S. V. Galaev, Yu. V. Shevtsova

Saratov State University, 83, Astrakhanskaya st., 410012, Saratov, Russia
Full-text PDF (165 kB) Citations (1)
References:
Abstract: The distribution $D$ of an almost contact metric structure $(\varphi,\vec\xi,\eta,g)$ is an odd analogue of the tangent bundle. In the paper an intrinsic symplectic structure naturally associated with the initial almost contact metric structure is constructed. The interior connection defines the parallel transport of admissible vectors (i.e. vectors belonging to the distribution $D$) along admissible curves. Each corresponding extended connection is a connection in the vector bundle $(D,\pi,X)$ defined by the interior connection and by an endomorphism $N:D\to D$. The choice of the endomorphism $N:D\to D$ determines the properties of the extended connection, whence those of the almost contact metric structure appearing on the space $D$ of the vector bundle $(D,\pi,X)$. It is shown that similarly to the bundle $TTX$, the tangent bundle $TD$ due to the fixation of the connection over the distribution (and later also the $N$-extended connection, i.e. connection in the vector bundle $(D,\pi,X)$) is decomposable in the direct sum of the vertical and horizontal distributions. Thus on the distribution $D$ the (extended) almost contact metric structure is defined in a natural way. The properties of the extended structure are investigated. In particular, it is proved that the extended almost contact structure is almost normal if and only if the distribution $D$ is a distribution of zero curvature.
Key words: contact structure, almost contact metric structure, interior symplectic connection, extended symplectic structure, almost contact Kaehlerian space.
Bibliographic databases:
Document Type: Article
UDC: 514.76
Language: Russian
Citation: S. V. Galaev, Yu. V. Shevtsova, “Almost contact metric structures defined by a symplectic structure over a distribution”, Izv. Saratov Univ. Math. Mech. Inform., 15:2 (2015), 136–141
Citation in format AMSBIB
\Bibitem{GalShe15}
\by S.~V.~Galaev, Yu.~V.~Shevtsova
\paper Almost contact metric structures defined by a symplectic structure over a~distribution
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2015
\vol 15
\issue 2
\pages 136--141
\mathnet{http://mi.mathnet.ru/isu574}
\crossref{https://doi.org/10.18500/1816-9791-2015-15-2-136-141}
\elib{https://elibrary.ru/item.asp?id=23647129}
Linking options:
  • https://www.mathnet.ru/eng/isu574
  • https://www.mathnet.ru/eng/isu/v15/i2/p136
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024