On the construction of the linearization of a nonlinear connection
Eduardo Mart\'inez
TL;DR
This paper explains how to construct a linear connection from a nonlinear connection on a vector bundle, clarifying its geometric interpretation and related concepts like parallel transport and curvature.
Contribution
It provides a detailed geometric construction of linearization of nonlinear connections using fiberwise linear approximation.
Findings
Clarifies the geometric meaning of linearized connections
Connects linearization to parallel transport and curvature
Provides a systematic construction method
Abstract
The construction of a linear connection on a pullback bundle from a connection on a vector bundle is explained in terms of fiberwise linear approximation. This procedure clarifies the geometric meaning of the linearized connection as well as the associated parallel transport and curvature.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons · Microtubule and mitosis dynamics