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On generalized Tanaka-Webster connection in Sasakian manifolds. (English) Zbl 1399.53039

Summary: The object of this paper is to characterize Sasakian manifolds admitting generalized Tanaka-Webster connection. We study certain curvature conditions of Sasakian manifolds with respect to the generalized Tanaka-Webster connection. Finally, we give an example of a 5-dimensional Sasakian manifold admitting the generalized Tanaka-Webster connection to illustrate the results.

MSC:

53C05 Connections (general theory)
53C20 Global Riemannian geometry, including pinching
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)