# zbMATH — the first resource for mathematics

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

##### MSC:
 53C35 Differential geometry of symmetric spaces 53B10 Projective connections
##### Keywords:
projectively symmetric manifold
Full Text:
##### References:
 [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). · JFM 53.0681.02 [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) [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.