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# Article

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Keywords:
contact metric manifolds; Tanaka connection; Jacobi operator
Summary:
In the present paper we investigate a contact metric manifold satisfying (C) $(\bar{\nabla }_{\dot{\gamma }}R)(\cdot ,\dot{\gamma })\dot{\gamma }=0$ for any $\bar{\nabla }$-geodesic $\gamma$, where $\bar{\nabla }$ is the Tanaka connection. We classify the 3-dimensional contact metric manifolds satisfying (C) for any $\bar{\nabla }$-geodesic $\gamma$. Also, we prove a structure theorem for a contact metric manifold with $\xi$ belonging to the $k$-nullity distribution and satisfying (C) for any $\bar{\nabla }$-geodesic $\gamma$.
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