## 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.)