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On almost pseudo symmetric manifolds. (English) Zbl 1224.53056
The authors introduce a new type of pseudo-Riemannian manifolds, called almost pseudo-symmetric manifold. Roughly speaking, their definition requires that the covariant derivatives of the type $$(0,4)$$ Riemannian curvature tensor $$\tilde{R}$$ can be combined from $$\tilde{R}$$ with the help of two non-zero 1-forms. If these 1-forms are equal, then one arrives at the class of pseudo-symmetric Riemannian manifolds introduced in M. C. Chaki [An. Ştiinţ. Univ. Al. I. Cuza Iaşi, N. Ser., Secţ. Ia 33, No. 1, 53–58 (1987; Zbl 0626.53037)]. The authors study this new type of pseudo-Riemannian manifolds under some extra conditions: 2-dimensional case, non-zero constant scalar curvature, cyclic Ricci tensor, Einstein condition and others. They also present some non-trivial examples.

##### MSC:
 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
##### Keywords:
almost pseudo-symmetric manifold