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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.)
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