Certain geometric properties of the cotangent bundle endowed with the horizontally deformed Sasaki metric

Abstract

This study presents a new family of Riemannian metrics on the cotangent bundle of a Riemannian manifold, referred to as horizontally deformed Sasaki metric. These metrics extend the classical Sasaki metric by incorporating a horizontal deformation. The paper conducts a detailed examination of the geometric structure of the cotangent bundle endowed with the horizontally deformed Sasaki metric, focusing on the Levi-Civita connection and various curvature tensors. Additionally, the geometry of a naturally arising hypersurface within the cotangent bundle is investigated through the derivation of its induced Levi-Civita connection and associated curvature formulas. The findings broaden the existing class of Riemannian metrics defined on cotangent bundles and provide deeper insight into the geometric framework of Riemannian manifolds and their cotangent structures. These contributions enhance the understanding of invariant metric structures on cotangent bundles and offer a foundation for further research in differential geometry.