本文中我們將介紹馬尤厄-卡當形式及卡當定理。接下來將其應用在海森堡群$H_1$，尤其著重在Pansu-Sphere上並計算高斯曲率。

In this thesis, we introduce the Maurer-Cartan form and the Cartan's theorem. We apply them on the Heisenberg group H_1, especially on the the Pansu-Sphere to calculate the Gaussian curvature.

Abstract(chinese)--------------------------I
Abstract-----------------------------------II
Contents-----------------------------------III
1.Introduction-----------------------------1
2.Main Theorem-----------------------------2
3.Example----------------------------------5
4.The Heisenberg Group H_1-----------------8
5.The Darboux Derivative on H_1------------11
6.The Codazzi-like Equation----------------18
7.Applications on the Pansu-Sphere---------20
Bibliography-------------------------------24

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3.Thomas A. Ivey; J. M. Landsberg, Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems, Graduate Studies in Mathematics, Volume 61, American Mathematical Society, 2003.
4.Chern S.S.; Chen W.H.; Lam K.S., Lectures on Differential Geometry, Series on University Mathematics, Vol.1, World Scientific Publishing Company, 1999.
5.Manfredo P. Do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Dover Publications, 2017.