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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Homogeneous spaces with
invariant projectively flat affine connections


Author: Hirohiko Shima
Journal: Trans. Amer. Math. Soc. 351 (1999), 4713-4726
MSC (1991): Primary 53C05, 53C30, 53C35, 53A15; Secondary 17C20
Published electronically: August 25, 1999
MathSciNet review: 1675234
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Abstract: We characterize invariant projectively flat affine connections in terms of affine representations of Lie algebras, and show that a homogeneous space admits an invariant projectively flat affine connection if and only if it has an equivariant centro-affine immersion. We give a correspondence between semi-simple symmetric spaces with invariant projectively flat affine connections and central-simple Jordan algebras.


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Additional Information

Hirohiko Shima
Affiliation: Department of Mathematics, Yamaguchi University, Yamaguchi 753-8512, Japan
Email: shima@po.cc.yamaguchi-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02523-4
PII: S 0002-9947(99)02523-4
Keywords: Invariant projectively flat affine connections, centro-affine immersions, homogeneous spaces, symmetric spaces, Jordan algebras
Received by editor(s): March 15, 1996
Published electronically: August 25, 1999
Article copyright: © Copyright 1999 American Mathematical Society