A fundamental differential system of Riemannian geometry

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Development of fundamental dynamics from differential geometry

The fundamental quantities of classical dynamics, such as position, velocity and acceleration, are expressed in terms of the Cartan tetrad, and the first Cartan structure equation is used to develop classical dynamics. The velocity is defined as the covariant exterior derivative of the position, and the acceleration as the exterior covariant derivative of the velocity. The resulting terms are a...

Ma Thema Tics : a . D . Michal " Riemannian " Differential Geometry In

Riemannian geometry

A Course in Riemannian Geometry