G-Steiner, co-Steiner and Normal Points of Bounded Euclidean Submanifolds

Abstract

The original ``Steiner point'', also known as the ``Steiner curvature centroid'', is the geometric centroid of the system obtained by placing a mass equal to the magnitude of the exterior angle at each vertex of a triangle. Steiner points have been studied and applied in networks, combinatorics, computational geometry and even in game theory. In this article, we extend the notion of Steiner point to the notion of g-Steiner point for a bounded Euclidean submanifolds with arbitrary codimension. In this article, we also introduce the notions of co-Steiner and normal points for bounded Euclidean submanifolds. We prove several basic properties for such points. Furthermore, we establish some links between g-Steiner, co-Steiner and normal points.