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Note on geodesics of cotangent bundle with Berger-type deformed Sasaki metric over Kählerian manifold (2303.01060v3)
Published 2 Mar 2023 in math.DG
Abstract: In this paper, first, we introduce the Berger-type deformed Sasaki metric on the cotangent bundle $T{\ast}M$ over a K\"{a}hlerian manifold $(M{2m}, J, g)$ and investigate the Levi-Civita connection of this metric. Secondly, we present the unit cotangent bundle equipped with Berger-type deformed Sasaki metric, and we investigate the Levi-Civita connection. Finally, we study the geodesics on the cotangent bundle and on unit cotangent bundle with respect to the Berger-type deformed Sasaki metric.