The Geometry of Quasi-Geodesics on Stiefel Manifolds

Differential geometry supplies important mathematical tools for engineering applications. Geodesics play a crucial role in many iterative methods and, when there are explicit formulas to write them, they provide elegant and computationally efficient methods to solve real problems. Unfortunately, for...

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Bibliographic Details
Published in2018 13th APCA International Conference on Automatic Control and Soft Computing (CONTROLO) pp. 213 - 218
Main Authors Jurdjevic, Velimir, Leite, Fatima Silva, Krakowski, Krzysztof
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.06.2018
Subjects
geodesics and quasi-geodesics
Geometry
horizontal distributions
Interpolation
Manifolds
Measurement
Optimal control
Radio frequency
Riemannian manifolds
Stiefel manifolds
sub-Riemannian problems
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Summary:Differential geometry supplies important mathematical tools for engineering applications. Geodesics play a crucial role in many iterative methods and, when there are explicit formulas to write them, they provide elegant and computationally efficient methods to solve real problems. Unfortunately, for some manifolds such formulas are hard to find. This is the case for the Stiefel manifold that plays an important role in computer vision and pattern recognition. Quasi-geodesics is another class of curves with constant geodesic curvature that have proved to be particularly useful to implement interpolating algorithms on Stiefel manifolds. The main objective of this paper is to reveal its interesting geometry, by showing their connection with solutions of a sub-Riemannian optimal control problem on a Lie group that acts on the manifold.
ISSN:2472-8489
DOI:10.1109/CONTROLO.2018.8514270