Geometric Configuration of Riemannian Submanifolds of arbitrary Codimension

Mohamed Abdelmalek, Mohammed Benalili, Kamil Niedziałomski

Published 2016-05-12Version 1

In this paper we study a geometric configuration of submanifolds of arbitrary codimension in an ambient Riemannian space. We obtain relations between the geometry of a q-codimension submanifold Mn along its boundary and the geometry of the boundary of Mn as an hypersuface of a q-codimensional submanifold Pn in an ambient space Mn+q. As a consequence of these geometric ralations we get that the ellipticity of the generalized Newton transformations implies the tranversality of Mn and Pn in Pn is totally geodesic in Mn+q.