A Four-manifold Approach to the Spherical Space Form Problem

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. ...

RICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM

Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...

Mechanical behaviour of motion for the two-dimensional monolayer system‎

‎In this paper we study the dynamics of the 2D-motion of a particle of monolayer‎. First we consider the usual physical time component and the plan manifold R2, having the polar coordinates. Then a geometric approach to nonholonomic constrained mechanical systems is applied to a problem from the two dimensional geometric dynamics of the Langmuir-Blodgett monolayer‎. We consider a constraint sub...

On images of continuous functions from a compact manifold to Euclidean space

Video Subject Inpainting: A Posture-Based Method

Despite recent advances in video inpainting techniques, reconstructing large missing regions of a moving subject while its scale changes remains an elusive goal. In this paper, we have introduced a scale-change invariant method for large missing regions to tackle this problem. Using this framework, first the moving foreground is separated from the background and its scale is equalized. Then, a ...