Einstein normal homogeneous Riemannian manifold

Some Einstein Homogeneous Riemannian Fibrations

We study the existence of projectable G-invariant Einstein metrics on the total space of G-equivariant fibrations M = G/L → G/K, for a compact connected semisimple Lie group G. We obtain necessary conditions for the existence of such Einstein metrics in terms of appropriate Casimir operators, which is a generalization of the result by Wang and Ziller about Einstein normal metrics. We describe b...

The Manifolds Covered by a Riemannian Homogeneous Manifold

The Conformal Transformation Group of a Compact Homogeneous Riemannian Manifold

On a class of paracontact Riemannian manifold

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

Fast Manifold Learning Based on Riemannian Normal Coordinates

We present a novel method for manifold learning, i.e. identification of the low-dimensional manifold-like structure present in a set of data points in a possibly high-dimensional space. The main idea is derived from the concept of Riemannian normal coordinates. This coordinate system is in a way a generalization of Cartesian coordinates in Euclidean space. We translate this idea to a cloud of d...