Projective structures on reductive homogeneous spaces

Podestà, Fabio

doi:10.1090/S0002-9939-1990-1013979-8

Projective structures on reductive homogeneous spaces
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by Fabio Podestà PDF

Proc. Amer. Math. Soc. 109 (1990), 1087-1096 Request permission

Abstract:

The aim of this work is to give a more direct and "geometric" proof of a theorem of Agaoka, that on a reductive homogeneous space $G/K$, every $G$-invariant projective structure admits a $G$-invariant affine connection. This connection can be chosen uniquely, subject to being torsionfree and satisfying one extra condition.

References

Yoshio Agaoka, Invariant flat projective structures on homogeneous spaces, Hokkaido Math. J. 11 (1982), no. 2, 125–172. MR 666751, DOI 10.14492/hokmj/1381757934
Luther Pfahler Eisenhart, Non-Riemannian geometry, American Mathematical Society Colloquium Publications, vol. 8, American Mathematical Society, Providence, RI, 1990. Reprint of the 1927 original. MR 1466961, DOI 10.1090/coll/008
Shoshichi Kobayashi and Tadashi Nagano, On projective connections, J. Math. Mech. 13 (1964), 215–235. MR 0159284
Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1996. Reprint of the 1963 original; A Wiley-Interscience Publication. MR 1393940
Katsumi Nomizu and Ulrich Pinkall, On a certain class of homogeneous projectively flat manifolds, Tohoku Math. J. (2) 39 (1987), no. 3, 407–427. MR 902579, DOI 10.2748/tmj/1178228287
I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685–697. MR 131248, DOI 10.1002/cpa.3160130408
Noboru Tanaka, Projective connections and projective transformations, Nagoya Math. J. 12 (1957), 1–24. MR 105154, DOI 10.1017/S0027763000021905