ON RICCI PSEUDO-SYMMETRIC MIXED QUASI-EINSTEIN HERMITIAN MANIFOLD

Resumo

The object of the present paper is to study the Bochner Ricci pseudosymmetric mixed quasi-Einstein Hermitian manifold (MQEH) and holomorphically projective Ricci pseudo-symmetric MQEH manifold. Also, it is shown that a Bochner Ricci pseudo-symmetric MQEH manifold is either a Bochner Ricci pseudo symmetric Einstein Hermitian manifold or B(Î¥1,Î¥2, Ï, σ) = Ls[A(Î¥2)C(Î¥1)−A(Î¥1)C(Î¥2)] holds. Further, for a holomorphically projective Ricci pseudo-symmetric MQEH manifold, if b ̸= 0 and K(Î¥1,Î¥2, Ï, σ) = 0 if and only if the vector fields Ï and σ corresponding to 1-forms A and C, respectively, are co-directional. Furthermore, we introduce and analyze the Bochner–holomorphically projective Ricci pseudo-symmetric cases, revealing additional
geometric constraints under which the vector fields Ï and σ must be co-directional or the manifold necessarily reduces to an Einstein manifold.”