On Finding Geodesic Equation of Normal Distribution and Gaussian Curvature  

作　　者：William W. S. Chen 

机构地区：[1]Department of Statistics, The George Washington University, Washington, USA

出　　处：《Applied Mathematics》2017年第9期1336-1342,共7页应用数学（英文）

摘　　要：In this paper, we apply two different algorithms to find the geodesic equation of the normal distribution. The first algorithm consists of solving a triply partial differential equation where these equations originated from the normal distribution. While the second algorithm applies the well-known Darboux Theory. These two algorithms draw the same geodesic equation. Finally, we applied Baltzer R.’s finding to compute the Gaussian Curvature.In this paper, we apply two different algorithms to find the geodesic equation of the normal distribution. The first algorithm consists of solving a triply partial differential equation where these equations originated from the normal distribution. While the second algorithm applies the well-known Darboux Theory. These two algorithms draw the same geodesic equation. Finally, we applied Baltzer R.’s finding to compute the Gaussian Curvature.

关 键 词：DARBOUX Theory DIFFERENTIAL Geometry GEODESIC EQUATION PARTIAL DIFFERENTIAL EQUATION NORMAL Distribution 

分 类 号：O1[理学—数学]