Acta Universitatis Danubius. Œconomica, Vol 4, No 1 (2008)

A Condition for a Sasakian Manifold to Be of Constant Curvature

Alin Cristian Ioan, Catalin Angelo Ioan


In this paper we give a generalization of some results due to T. Takahashi [5] and M. Okumura [4]. Explicitly, we study an equation of the form R(X,Y)A=0 where X,Y are arbitrary vector fields on a Sasakian manifold and A a (1,3)-tensor field which generalizes the Riemann curvature tensor, Weyl conformal curvature tensor, Weyl projective curvature tensor and Yano concircular curvature tensor. The result which we obtain says that in complementary conditions the manifold is of constant curvature.


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