On weakly projective symmetric manifolds. (English) Zbl 1224.53039

Shaikh, A. A.; Hui, Shyamal Kumar

Acta Math. Acad. Paedagog. Nyházi. (N.S.) 25, No. 2, 247-269 (2009).

Summary: The object of the present paper is to study weakly projective symmetric manifolds and its decomposability with several non-trivial examples. Among others it is shown that in a decomposable weakly projective symmetric manifold both the decompositions are weakly Ricci symmetric.

MSC:

53B35	Local differential geometry of Hermitian and Kählerian structures
53B05	Linear and affine connections
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords:

weakly projective symmetric manifold; weakly Ricci symmetric manifold; projective curvature tensor; decomposable manifold; scalar curvature