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On a quarter-symmetric non-metric connection in a Lorentzian para-cosymplectic manifold. (English) Zbl 1228.53041

From the authors’ abstract: We define and study a quarter-symmetric non-metric connection on an LP-cosymplectic manifold. The curvature tensor and the Ricci tensor of the quarter-symmetric non-metric connection is found. A necessary and sufficient condition is deduced for the Ricci tensor \(\overline\nabla\) to be symmetric and skew-symmetric under certain conditions. The first and the second Bianchi identity are associated with a quarter-symmetric non-metric connection \(\overline\nabla\). The Weyl conformal curvature tensor and the special curvature tensor of a quarter-symmetric non-metric connection \(\overline\nabla\) are found.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53B05 Linear and affine connections
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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