zbMATH — the first resource for mathematics

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.

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)