Berger type deformed Sasaki metric on the cotangent bundle
Commun. Korean Math. Soc. 2021 Vol. 36, No. 3, 575-592
Published online May 12, 2021
Printed July 31, 2021
Abderrahim Zagane
University Center of Relizane
Abstract : In this paper, we introduce the Berger type deformed Sasaki metric on the cotangent bundle $T^{\ast}M$ over an anti-paraK\"{a}hler manifold $(M, \varphi, g)$ as a new natural metric with respect to $g$ non-rigid on $T^{\ast}M$. Firstly, we investigate the Levi-Civita connection of this metric. Secondly, we study the curvature tensor and also we characterize the scalar curvature.
Keywords : Horizontal lift, vertical lift, cotangent bundles, Berger type deformed Sasaki metric, curvature tensor
MSC numbers : 53C07, 53C55, 53B35, 53A45
Supported by : This note was supported by National Algerian PRFU project.
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