Gauss-Bonnet theorems in the generalized affine group and the generalized BCV spaces

Tong Wu; Yong Wang; Tong Wu; Yong Wang

doi:10.3934/math.2021678

AIMS Mathematics

2021, Volume 6, Issue 11: 11655-11685. doi: 10.3934/math.2021678

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Research article

Gauss-Bonnet theorems in the generalized affine group and the generalized BCV spaces

Tong Wu ,
Yong Wang ^,

School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received: 15 March 2021 Accepted: 06 August 2021 Published: 11 August 2021
MSC : 53C40, 53C42

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.
- the generalized affine group,
- the generalized BCV spaces,
- Gauss-Bonnet theorem,
- sub-Riemannian limit
Citation: Tong Wu, Yong Wang. Gauss-Bonnet theorems in the generalized affine group and the generalized BCV spaces[J]. AIMS Mathematics, 2021, 6(11): 11655-11685. doi: 10.3934/math.2021678

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Abstract

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.

References

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