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arXiv · 2102.01907

Affine connections and Gauss-Bonnet theorems in the Heisenberg group

Yong Wang
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Abstract

In this paper, we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean $C^2$-smooth surface in the Heisenberg group away from characteristic points and signed geodesic curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for Euclidean $C^2$-smooth curves on surfaces. We get Gauss-Bonnet theorems associated to two kinds of Schouten-Van Kampen affine connections in the Heisenberg group.

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Yong Wang. 2021-02-03. Affine connections and Gauss-Bonnet theorems in the Heisenberg group. https://arxiv.org/abs/2102.01907

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