TY - JOUR
AU1 - Mietton, Thomas
AU2 - Rizzi, Luca
AB - 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.
TI - Branching Geodesics in Sub-Riemannian Geometry
JF - Geometric and Functional Analysis
DO - 10.1007/s00039-020-00539-z
DA - 2020-08-09
UR - https://www.deepdyve.com/lp/springer-journals/branching-geodesics-in-sub-riemannian-geometry-HDyjl8gvEF
SP - 1139
EP - 1151
VL - 30
IS - 4
DP - DeepDyve
ER -