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Frame bundle
About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.
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19 citations
TL;DR: In this article, the fibre derivative of a bundle map is studied in detail, and a geometric construction useful to solve the Euler-Lagrange equation for a singular lagrangian is presented.
19 citations
TL;DR: In this paper, the Burger-Roblin measure is ergodic for the frame bundle of a non-elementary convex cocompact hyperbolic 3-manifold if and only if δ > 1.
Abstract: Let M be a non-elementary convex cocompact hyperbolic 3-manifold and δ be the critical exponent of its fundamental group. We prove that a one-dimensional unipotent flow for the frame bundle of M is ergodic for the Burger-Roblin measure if and only if δ > 1.
19 citations
TL;DR: In this article, a coordinate-free proof of the maximum principle is provided in the specific case of an optimal control problem with fixed time, which heavily relies on a special notion of variation of curves that consist of a concatenation of integral curves of time-dependent vector fields with unit time component.
Abstract: A coordinate-free proof of the maximum principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of integral curves of time-dependent vector fields with unit time component, and on the use of a concept of lift over a bundle map. We further derive necessary and sufficient conditions for the existence of so-called abnormal extremals.
19 citations
19 citations