The Warped Product of Hamiltonian Spaces

TL;DR

This paper introduces the concept of warped products in Hamilton spaces, explores their geometric properties, and establishes conditions under which these spaces relate to Riemannian manifolds, expanding the understanding of Hamiltonian geometry.

Contribution

It defines warped product Hamilton spaces and investigates their geometric structures and relations to base Hamiltonian manifolds, providing new theoretical insights.

Findings

Warped product Hamilton spaces can be endowed with Hamiltonian structures.

The geometric properties such as nonlinear connections are characterized.

The Sasaki lifted metric is bundle-like iff base spaces are Riemannian.

Abstract

In this work, the warped product of Hamilton spaces is introduced and it is shown that these spaces obtain Hamiltonian structure as well. Then, the geometric properties of warped product Hamilton spaces such as their nonlinear connections and natural cotangent bundle structures are studied. Moreover, we prove some theorems that show geometric relation between warped product Hamiltonian space and its base Hamiltonian manifolds. For example, we prove that for non-constant warped function $f$, the sasaki lifted metric $G$ of Hamiltonian warped product space is bundle-like for its vertical foliation if and only if based Hamiltonian spaces are Riemannian manifolds.