Some Results on Riemannean Multiple Barycenters

Mostafa Zahri, Naji Khallaf

Department of Mathematics, College of Science, Taibah University, Madinah, Saudi Arabia.

DOI: 10.4236/jamp.2014.27058                

Abstract

A characteristic of a special case of Riemannean barycenters on the unit circle is presented. The non-uniqueness of such barycenters leads to an interesting study of the so-called multiple barycenters. In this work, we deal with a smooth one-dimensional manifold S¹ only. Some theoretical and computational analysis is listed.

Keywords

Smooth Manifold, Geodesic, Barycenter of Masses, Metric Space, Multiple Barycenters

Conflicts of Interest

The authors declare no conflicts of interest.

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