Quarter-Symmetric Metric Connection on a Cosymplectic Manifold

Miroslav D. Maksimović () and Milan Lj. Zlatanović
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Miroslav D. Maksimović: Department of Mathematics, Faculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia
Milan Lj. Zlatanović: Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia

Mathematics, 2023, vol. 11, issue 9, 1-12

Abstract: We study the quarter-symmetric metric A -connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to the quarter-symmetric metric A -connection, we construct the Weyl projective curvature tensor on a cosymplectic manifold. In this way, we obtain new conditions for the manifold to be projectively flat. At the end of the paper, we define η -Einstein cosymplectic manifolds of the θ -th kind and prove that they coincide with the η -Einstein cosymplectic manifold.

Keywords: almost-contact manifold; cosymplectic manifold; co-Kähler manifold; quarter-symmetric connection; ? -Einstein manifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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