Tohoku Mathematical Journal
2024
September
SECOND SERIES VOL. 76, NO. 3

Tohoku Math. J.
76 (2024), 411-421

Title QUASI CONTACT METRIC MANIFOLDS SATISFYING A NULLITY CONDITION

Author Fereshteh Malek and Rezvan Hojati

(Received November 24, 2022, revised February 3, 2023)
Abstract. A quasi contact metric manifold in some sense is a generalization of contact metric manifold. There is an open question whether quasi contact metric manifolds of dimension greater than 3 are contact metric or not. In this paper, we show that the answer is positive for ones of dimension $> 5$ when the Riemannian curvature tensor in the direction of the characteristic vector field satisfies the nullity condition (*), and then study the Riemannian and Ricci curvature in the 5-dimensional case.

Mathematics Subject Classification. Primary 53C15; Secondary 53C25, 53D10, 53D15.
Key words and phrases. Contact metric manifold, quasi contact metric manifold, nullity condition, $(\kappa,\mu)$-space.

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