Projectively symmetric spaces. (English) Zbl 0697.53048

The main result: Any complete Riemannian manifold which is locally symmetric, globally properly projectively symmetric and projectively homogeneous is projectively equivalent to the standard sphere \(S^ n\) or to the real projective space \({\mathbb{R}}P^ n\).
Reviewer: O.Kowalski


53C35 Differential geometry of symmetric spaces
53B10 Projective connections
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[1] Gupta, B., On projective symmetric spaces, J. Austr. Math. Soc., 4, 113-121 (1964) · Zbl 0126.17802
[2] L. P.Eisenhart,Non-Riemannian geometry, Amer. Soc. Colloq. Publ.,8 (1927).
[3] S.Kobayashi,Transformation groups in differential geometry, Ergebnisse der Mathematik, Springer-Verlag (1972). · Zbl 0246.53031
[4] Kobayashi, S., Projective structures of hyperbolic type, Banach Centre Publ., 12, 127-152 (1984) · Zbl 0558.53019
[5] O.Kowalski,Generalized symmetric spaces, Lecture Notes in Mathematics, Springer-Verlag (1980). · Zbl 0431.53042
[6] Nagano, T., The projective transformation on a space with parallel Ricci tensor, Kodai Math. Sem. Rep., 11, 131-138 (1959) · Zbl 0097.37503
[7] Ishihara, S., Groups of projective transformations and groups of conformal transformations, J. Math. Soc. Japan, 9, 195-227 (1957) · Zbl 0080.37401
[8] Yano, K.; Nagano, T., Some theorems on projective and conformal transformations, Indag. Math., 19, 451-458 (1957) · Zbl 0079.15603
[9] Wu, H., Some theorems on projectively hyperbolicity, J. Math. Soc. Japan, 33, 79-104 (1981) · Zbl 0458.53016
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