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The sub‐Riemannian cut locus of H ‐type groups
Author(s) -
Autenried Christian,
Godoy Molina Mauricio
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400368
Subject(s) - mathematics , locus (genetics) , totally geodesic , geodesic , disjoint sets , pure mathematics , nilpotent , type (biology) , group (periodic table) , combinatorics , mathematical analysis , ecology , biochemistry , chemistry , organic chemistry , biology , gene
In the present paper we prove that the sub‐Riemannian cut locus at the origin of a wide class of nilpotent groups of step two, called H ‐type groups, corresponds to the center of the group. We obtain this result by completely describing the sub‐Riemannian geodesics in the group, and using these to obtain three disjoint sets of points in the group determined by the number of geodesics joining them to the origin.