Geodesic and F-Geodesic Exploration with a Vertical Generalized Berger-Type Deformed Sasaki Metric on the Tangent and ϕ-Unit Tangent Bundles

Abstract

In this research paper, we delve into a comprehensive exploration of geodesics and F-geodesics inquiries. Our investigation centers around a vertical generalized Berger-type deformed Sasaki metric, which is applied to both the tangent bundle TM and the ϕ-unit tangent bundle T₁^{ϕ}M. These bundles are situated over an anti-paraKähler manifold (M^{2m},ϕ,g).