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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1977, Volume 22, Issue 5, Pages 633–642 (Mi mz8087)

Morphisms of geometric structures

P. Ya. Grushko

Irkutsk State University

Abstract: The concept of $\{G,\rho,V\}$-structure is introduced which is a principal $G$-bundle B on which a $V$-valued form is given. If the representation $\rho$ of the group $G$ on the vector space $V$ is faithful and the fibration $B\to B\pmod G$ is locally trivial, then the $\{G,\rho,V\}$-structure is equivalent to some $G$-structure. The relation between local and global transitivity of the structure is studied under the condition that the space of the structure is compact and simply connected. It is proved that the universal covering space of a $\{G,\rho,V\}$-structure can be viewed as a $\{G',\rho',V\}$-structure.

Full text: PDF file (806 kB)

English version:
Mathematical Notes, 1977, 22:5, 844–849

Bibliographic databases:

UDC: 513

Citation: P. Ya. Grushko, “Morphisms of geometric structures”, Mat. Zametki, 22:5 (1977), 633–642; Math. Notes, 22:5 (1977), 844–849

Citation in format AMSBIB
\Bibitem{Gru77} \by P.~Ya.~Grushko \paper Morphisms of geometric structures \jour Mat. Zametki \yr 1977 \vol 22 \issue 5 \pages 633--642 \mathnet{http://mi.mathnet.ru/mz8087} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=478056} \zmath{https://zbmath.org/?q=an:0365.53010} \transl \jour Math. Notes \yr 1977 \vol 22 \issue 5 \pages 844--849 \crossref{https://doi.org/10.1007/BF01098347}