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On concircular transformations in Riemannian spaces

Part of: Local differential geometry Classical differential geometry

Published online by Cambridge University Press:  09 April 2009

Luo Chongshan
Luo Chongshan
Affiliation:
Department of Mathematics, Sichuan Teachers' College, Chengdu, People's Republic of China
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Abstract

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This paper introduces a tensor that contains the Riemannian curvature tensor and the conformal curvature tensor as special examples in the Riemannian space (Mn, g), and by using this tensor we define C-semi-symmetric space. In this paper, we have the following main result: if there is a non-trivial concircular transformation between two C-semi-symmetric spaces, then both spaces are of quasi-constant curvature.

MSC classification

Secondary: 53B20: Local Riemannian geometry 53A30: Conformal differential geometry
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 2 , April 1986 , pp. 218 - 225
Copyright
Copyright Australian Mathematical Society 1986

References

1Yano, K., Concircular transformation, Proc. Imp. Acad. Tokyo 16 (1940), 195200 and 254360.Google Scholar
2Eisenhart, L. P., Riemannian geometry (Princeton University Press, 1949).Google Scholar
3Venzi, P., On concircular mappings in Riemannian and pseudo-Riemannian manifolds with symmetric conditions, Tensor (N.S.) 33 (1979), 109113.Google Scholar
4Wang, Yuen-da, On some properties of Riemannian spaces of quasi-constant curvature, Tensor (N.S.) 35 (1981), 173176.Google Scholar
5Cheng-chung, Hwang, Some theorems on the spaces of quasi-constant curvature, Mathematical Research and Exposition (China) 3 (1983), No. 1, 116.Google Scholar