Hokkaido Mathematical Journal

Projectively flat connections and flat connections on homogeneous spaces

Hajime URAKAWA

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Abstract

We show a correspondence between the set of all $G$-invariant projectively flat connections on a homogeneous space $M=G/K$, and the one of all $\widetilde{G}$-invariant flat connections on homogeneous spaces $\widetilde{M}=\widetilde{G}/K$, where $\widetilde{G}$ is a central extension of $G$ (Theorem 3.3).

Article information

Source
Hokkaido Math. J. Volume 39, Number 2 (2010), 139-155.

Dates
First available in Project Euclid: 24 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1277385658

Digital Object Identifier
doi:10.14492/hokmj/1277385658

Mathematical Reviews number (MathSciNet)
MR2665158

Zentralblatt MATH identifier
1222.53057

Subjects
Primary: 53A15: Affine differential geometry
Secondary: 53C35: Symmetric spaces [See also 32M15, 57T15] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}

Keywords
projectively flat connection flat connection reductive homogeneous space symmetric space simple Lie group

Citation

URAKAWA, Hajime. Projectively flat connections and flat connections on homogeneous spaces. Hokkaido Math. J. 39 (2010), no. 2, 139--155. doi:10.14492/hokmj/1277385658. https://projecteuclid.org/euclid.hokmj/1277385658


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