Research Article

Concircularly semi-symmetric metric connection

Published in: Quaestiones Mathematicae
Volume 47 , issue 3 , 2024 , pages: 557–576

DOI: 10.2989/16073606.2023.2230369

Author(s): Miroslav D. Maksimović University of Priština in Kosovska Mitrovica, Serbia , Miloš Z. Petrović University of Niš, Serbia , Nenad O. Vesić Mathematical Institute of Serbian Academy of Sciences and Arts, University of Belgrade, , Milan Lj. Zlatanović University of Niš, Serbia

Keywords: Primary: 53B05 , Secondary: 53C05 , Concircular curvature tensor , concircular vector , Einstein manifold , Riemannian manifold , semi-symmetric connection , Weyl projective curvature tensor

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Abstract

Results on a concircularly semi-symmetric metric connection on a Riemannian manifold are presented. Six linearly independent curvature tensors with respect to this non-symmetric linear connection are studied, and the tensors coincident with the Weyl projective curvature tensor and the concircular curvature tensor of the Levi-Civita connection are determined. Transformations of connections when the Riemannian curvature tensor, Weyl projective curvature tensor and the concircular curvature tensor of the Levi-Civita connection are invariant are also observed. Moreover, new conditions for the Einstein manifold are derived.

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