Quarter-symmetric non-metric connection

2022/10/04 by Miroslav D. Maksimović, Maksimović, Miroslav
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2210.01509

openalex publication_date 2022/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper will study a new quarter-symmetric non-metric connection on a generalized Riemannian manifold. It will determine the relations that the torsion tensor satisfies. The exterior derivative of the skew-symmetric part F of basic tensor G with respect to the Levi-Civita connection coincides with that of skew-symmetric part F with respect to quarter-symmetric non-metric connection, which implies that the even-dimensional manifold endowed with F is symplectic manifold if and only if it is closed with respect to quarter-symmetric non-metric connection. The linearly independent curvature tensors of this connection and its dual connection are determined and the properties of these tensors are discussed. Finally, the condition is given that the connection should be dual symmetric.

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