A note on flat nonholonomic Riemannian structures on three-dimensional Lie groups

A note on flat nonholonomic Riemannian structures on three-dimensional Lie groups

We consider flat nonholonomic Riemannian manifolds, i.e., those whose associated parallel transport (induced by the nonholonomic connection) is path-independent. We first characterize flatness for structures on three-dimensional manifolds, and hence classify the flat left-invariant structures on sim...

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Veröffentlicht in:Beiträge zur Algebra und Geometrie 2019-09, Vol.60 (3), p.419-436
Hauptverfasser: Barrett, Dennis I., Remsing, Claudiu C.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algebraic Geometry
Convex and Discrete Geometry
Geometry
Lie groups
Mathematics
Mathematics and Statistics
Original Paper
Riemann manifold
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Zusammenfassung:We consider flat nonholonomic Riemannian manifolds, i.e., those whose associated parallel transport (induced by the nonholonomic connection) is path-independent. We first characterize flatness for structures on three-dimensional manifolds, and hence classify the flat left-invariant structures on simply connected Lie groups.
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-018-0421-7