TITLE:
On Finding Geodesic Equation of Normal Distribution and Gaussian Curvature
AUTHORS:
William W. S. Chen
KEYWORDS:
Darboux Theory, Differential Geometry, Geodesic Equation, Partial Differential Equation, Normal Distribution
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.9,
September
27,
2017
ABSTRACT: 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.