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math.DG2026
Connection Towers and Sasaki Metrics on Higher-Order Tangent Bundles
Margarida Camarinha, Jacob R. Goodman
Higher-order tangent bundles possess a rich tower of fibrations, suggesting the existence of geometric structures compatible with their iterated bundle structure. In this paper, we…
math.MG2026
Riemannian Metric Preconditioning for Trajectory Tracking
Jacob R. Goodman, Hajg Jasa
We introduce a rank-one Riemannian cometric update inducing a modification of the Riemannian metric that makes specific directions of motion cheaper to travel along. We establish b…
math.MG2026
A Generalized Sasaki Metric on the Second-Order Tangent Bundle
Margarida Camarinha, Jacob R. Goodman
This paper constructs a connection map on the second-order tangent bundle induced by a linear connection on the base manifold and uses it to define a generalized Sasaki metric. The…