Abstract
In this paper, we compute sub-Riemannian limits of Gaussian curvature for a Euclidean C2-smooth surface in the affine group and the group of rigid motions of the Minkowski plane away from characteristic points and signed geodesic curvature for Euclidean C2-smooth curves on surfaces. We get Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane.
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Acknowledgements
The first author was supported by National Natural Science Foundation of China (Grant No. 11771070). The authors are deeply grateful to the referees for their valuable comments and helpful suggestions.
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Wang, Y., Wei, S. Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane. Sci. China Math. 64, 1843–1860 (2021). https://doi.org/10.1007/s11425-019-1667-5
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DOI: https://doi.org/10.1007/s11425-019-1667-5