## On generalized Sasakian-space-forms with Weyl-conformal curvature tensor.(English)Zbl 1257.53072

Summary: The object of the this paper is to study Weyl-pseudosymmetric generalized Sasakians pace-forms and space-forms satisfying the conditions $$C(\xi,X)R = 0$$ and $$C(\xi,X)S = 0$$, where $$C$$ is the Weyl-conformal curvature tensor, $$R$$ and $$S$$ are the Riemannian curvature tensor and the Ricci tensor of the space-form respectively.

### MSC:

 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
Full Text:

### References:

 [1] P. Alegre, D. Blair, and A. Carriazo, Israel J. Math. 14, 157 (2004). · Zbl 1064.53026 [2] P. Alegre and A. Carriazo, Differential Geom. and its application, 26, 656 (2008); doi. 10.1016/j difgeo. · Zbl 1156.53027 [3] D. E. Blair, Contact manifolds in Riemannian Geometry (Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin, 1976). · Zbl 0319.53026 [4] U. C. De and A. Sarkar, Thai J.Math. 8(1), 1 (2010). [5] U. C. De and A. Sarkar, QuaestionesMathematicae 33(2), 245 (2010). [6] U. C. De and A. Sarkar, Some curvature properties of generalized Sasakian-space-forms, To appear in International Journal ofMathematical Sciences. · Zbl 1254.53077 [7] R. Deszcz, Bull. Soc. math. Belg. Ser. A., 44, 1 (1992). [8] R. Desczc and W. Grycak, Bull. Inst.Math. Acad. Sinica. 15, 311 (1987). [9] U. K. Kim, Note di matemetica 26, 55 (2006). [10] K. Nomizu, TohokuMath. J. 20, 46 (1968). · Zbl 0174.53301 [11] Y. A. Ogawa, Natur. Sci. Report, Ochanomizu Univ. 28, 21 (1977). [12] Z. I. Szabo, J. Diff. Geom. 17, 531 (1982). · Zbl 0508.53025 [13] S. Tanno, Proc. Japan Acad. 43, 581 (1967). · Zbl 0155.49802 [14] K. Yano and M. Kon, Structures on manifolds (Series inMath., 3, World Sci., 1984). · Zbl 0557.53001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.