The Pilgerschritt (Liedl) Transform on Manifolds

Wolfgang Förg-Rob ()
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Wolfgang Förg-Rob: University of Innsbruck

A chapter in Applications of Nonlinear Analysis, 2018, pp 335-353 from Springer

Abstract: Abstract Finding geodesic lines connecting two points on a manifold with linear connection is usually done by shooting methods. In the last seventieth R. Liedl hat the idea to choose an arbitrary path between these two points and transforming it in order to get the geodesic line. He worked out this method for Lie groups, and in this paper the generalization to manifolds is given together with a convergence theorem that locally this method can be achieved in order to approximate geodesic lines.

Keywords: Linear Connection; Geodesic Line; Coordinate Expression; Iterative Root Finding; Parallel Transport (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-89815-5_11

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DOI: 10.1007/978-3-319-89815-5_11

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