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Quarter-symmetric metric connection on a Sasakian manifold. (English) Zbl 1025.53013
A linear metric connection on a Riemannian manifold $$M$$ is called quarter-symmetric if its torsion tensor $$T$$ satisfies $$T(X,Y) = \pi(Y)F(X) - \pi(X)F(Y)$$ with some one-form $$\pi$$ and $$(1,1)$$-tensor field $$F$$ on $$M$$. The authors investigate the existence problem of quarter-symmetric metric connections and study curvature properties of such connections on Sasakian manifolds.

##### MSC:
 53C05 Connections, general theory 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)