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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 1, Pages 3–37 (Mi izv955)  

Twistors and $G$-structures

D. V. Alekseevskiia, M. M. Graev

a International Center "Sophus Lie"

Abstract: The authors distinguish a class of twistor spaces $Z=P\times_GS$ that are associated, following Berard-Bergery and Ochiai, with $G$-structures $P$ on even-dimensional manifolds and connections in $P$. It is assumed that $S=G/H$ is a complex totally geodesic submanifold of the affine symmetric space $\operatorname{GL_{2n}}(\mathbf R)/\operatorname{GL_n}(\mathbf C)$. This class includes all the basic examples of twistor spaces fibered over an even-dimensional base. The integrability of the canonical almost complex structure $J_Z$ and the holomorphy of the canonical distribution $\mathscr H_Z$ in $Z$ are studied in terms of some natural $H$-structure with a connection on the manifold $Z$. Some examples are also treated.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 40:1, 1–31

Bibliographic databases:

UDC: 514.76
MSC: Primary 53C10, 53C15, 53C35, 58E20; Secondary 32L25, 22E45, 58A30, 32M10
Received: 03.04.1991

Citation: D. V. Alekseevskii, M. M. Graev, “Twistors and $G$-structures”, Izv. RAN. Ser. Mat., 56:1 (1992), 3–37; Russian Acad. Sci. Izv. Math., 40:1 (1993), 1–31

Citation in format AMSBIB
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\by D.~V.~Alekseevskii, M.~M.~Graev
\paper Twistors and $G$-structures
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
\issue 1
\pages 3--37
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..40....1A}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 40
\issue 1
\pages 1--31
\crossref{https://doi.org/10.1070/IM1993v040n01ABEH001851}
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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