Geodesic
Asymptotic behaviour of the sphere and front of a~flat sub-Riemannian structure on the Martinet distribution
Sbornik. Mathematics, Tome 213 (2022) no. 5, pp. 624-640

Voir la notice de l'article provenant de la source Math-Net.Ru

The sphere and front of a flat sub-Riemannian structure on the Martinet distribution are surfaces with nonisolated singularities in three-dimensional space. The sphere is a subset of the front; it is not subanalytic at two antipodal points (the poles). The asymptotic behaviour of the sub-Riemannian sphere and Martinet front are calculated at these points: each surface is approximated by a pair of quasihomogeneous surfaces with distinct sets of weights in a neighbourhood of a pole. Bibliography: 13 titles.
Keywords: sphere of a sub-Riemannian structure, front of a sub-Riemannian structure, exponential map, Jacobi elliptic functions.
Mots-clés : Martinet distribution 
@article{SM_2022_213_5_a2,
     author = {I. A. Bogaevsky},
     title = {Asymptotic behaviour of the sphere and front of a~flat {sub-Riemannian} structure on the {Martinet} distribution},
     journal = {Sbornik. Mathematics},
     pages = {624--640},
     publisher = {mathdoc},
     volume = {213},
     number = {5},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2022_213_5_a2/}
}
TY  - JOUR
AU  - I. A. Bogaevsky
TI  - Asymptotic behaviour of the sphere and front of a~flat sub-Riemannian structure on the Martinet distribution
JO  - Sbornik. Mathematics
PY  - 2022
SP  - 624
EP  - 640
VL  - 213
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2022_213_5_a2/
LA  - en
ID  - SM_2022_213_5_a2
ER  - 
%0 Journal Article
%A I. A. Bogaevsky
%T Asymptotic behaviour of the sphere and front of a~flat sub-Riemannian structure on the Martinet distribution
%J Sbornik. Mathematics
%D 2022
%P 624-640
%V 213
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2022_213_5_a2/
%G en
%F SM_2022_213_5_a2
I. A. Bogaevsky. Asymptotic behaviour of the sphere and front of a~flat sub-Riemannian structure on the Martinet distribution. Sbornik. Mathematics, Tome 213 (2022) no. 5, pp. 624-640. http://geodesic.mathdoc.fr/item/SM_2022_213_5_a2/