Based on the Riemannian geometry theory, a novel conformal transformation was proposed and the kernel function was modified by the transformation in a data-dependent way.

It can be excluded with data dependent way based on Riemannian geometry for improved SVM.

Two novel conformal transformations were proposed based on the Riemannian geometry theory and S.

A simple proof of finiteness of areas of asymptotic triangles in non-Euclidean geometry;

From the study of the parallel postulate to the establishment of the non-Euclidean geometry;

Extend of non-euclidean geometry form upon tradition space

wA mathematical model so called “Poincaré Model” is introduced to solve these problems by using the theorems of Euclidean geometry stead of Non Euclidean geometry.