In this note, we show that sub-Riemannian manifolds can contain branching normal minimizing geodesics. This phenomenon occurs if and only if a normal geodesic has a discontinuity in its rank at a non-zero time, which in particular for a strictly normal geodesic means that it contains a non-trivial abnormal subsegment. The simplest example is obtained by gluing the three-dimensional Martinet flat structure with the Heisenberg group in a suitable way. We then use this example to construct more general types of branching.

Branching Geodesics in Sub-Riemannian Geometry / Mietton, T.; Rizzi, L.. - In: GEOMETRIC AND FUNCTIONAL ANALYSIS. - ISSN 1016-443X. - 30:(2020), pp. 1139-1151. [10.1007/s00039-020-00539-z]

Branching Geodesics in Sub-Riemannian Geometry

Rizzi, L.
2020

Abstract

In this note, we show that sub-Riemannian manifolds can contain branching normal minimizing geodesics. This phenomenon occurs if and only if a normal geodesic has a discontinuity in its rank at a non-zero time, which in particular for a strictly normal geodesic means that it contains a non-trivial abnormal subsegment. The simplest example is obtained by gluing the three-dimensional Martinet flat structure with the Heisenberg group in a suitable way. We then use this example to construct more general types of branching.
30
1139
1151
https://arxiv.org/abs/2002.12293
Mietton, T.; Rizzi, L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/128683
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