Open AccessGauss-Bonnet theorems in the generalized affine group and the generalized BCV spaces
Author(s) -
Tong Wu,
Yong Wang
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021678
Subject(s) - mathematics , gaussian curvature , affine transformation , pure mathematics , heisenberg group , euclidean geometry , group (periodic table) , geodesic , curvature , mathematical analysis , geometry , physics , quantum mechanics
In this paper, we compute sub-Riemannian limits of Gaussian curvature for a Euclidean $ C^2 $-smooth surface in the generalized affine group and the generalized BCV spaces away from characteristic points and signed geodesic curvature for Euclidean $ C^2 $-smooth curves on surfaces. We get Gauss-Bonnet theorems in the generalized affine group and the generalized BCV spaces.