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On weakly symmetric Riemannian spaces. (English) Zbl 0797.53041
A Riemannian space $$V_ n$$ is locally symmetric if $$\nabla R = 0$$. Consecutive weakening of this gives $$V_ n$$ with recurrent curvature, pseudo-symmetric (p.s.) $$V_ n$$ [M. C. Chaki, An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Nouv. Sér., Secţ. Ia 33, No. 1, 53-58 (1987; Zbl 0626.53037)], and weakly symmetric (w.s.) $$V_ n$$ [L. Tamássy and the author, Colloq. Math. Soc. János Bolyai 56, 663-670 (1992; Zbl 0791.53021)] concerning p.s. $$V_ n$$ are transferred to a w.s. $$V_ n$$.

MSC:
 53C35 Differential geometry of symmetric spaces 53B20 Local Riemannian geometry