Weak Quasi-Contact Metric Manifolds and New Characteristics of K-Contact and Sasakian Manifolds

Vladimir Rovenski ()
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Vladimir Rovenski: Department of Mathematics, University of Haifa, Haifa 3498838, Israel

Mathematics, 2024, vol. 12, issue 20, 1-9

Abstract: Quasi-contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of contact metric manifolds. Weak almost-contact metric manifolds, i.e., where the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, have been defined by the author and R. Wolak. In this paper, we study a weak analogue of quasi-contact metric manifolds. Our main results generalize some well-known theorems and provide new criterions for K-contact and Sasakian manifolds in terms of conditions on the curvature tensor and other geometric objects associated with the weak quasi-contact metric structure.

Keywords: quasi-contact metric manifold; K-contact manifold; Sasakian manifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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