高维非欧空间中的Darboux定理

Darboux's theorem in high-dimensional non-Euclidean space

利用度量几何的理论和方法以及非欧几何的射影模型研究球面空间和双曲空间两个n维单形的体积公式,将欧氏几何中著名的Darboux定理推广到n维常曲率空间的两个n维单形中,获得球面空间和双曲空间两个n维单形的广义体积公式.

By using the theory and methed of metric geometry and projective model of non-Euclidean space, a volume formula of evaluating two n-dimensional simplexes in spherical and hyperbolic space was investigated and the well-known Darboux＇s theorem in Euclidean geometry was generalized to these two simplexes in n-dimensional space with constant curature so that the volume evaluation formula of two simplexes in the spherical and hyperbolic space was obtained.