Gauss-Bonnet theorem connects the intrinsic differential geometry of a surface with its topology and has many applications in physics and mathematics. Recently, Balogh et al. used a Riemannian approximation scheme to prove a Heisenberg version of the Gauss-Bonnet theorem. Inspired by this work, Professor Wang and Wei investigated sub-Riemannian geometries of some typical spaces such as the affine group, the group of rigid motions of the Minkowski plane, the BCV spaces and the Lorentzian Heisenberg group, and proved Gauss-Bonnet theorems in these Lie groups. In this talk, we plan to introduce some results on Gauss-Bonnet theorems in three-dimensional Riemannian Lie groups such as roto-translation group and Lorentzian Sasakian space forms.

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