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arXiv · 1605.03875

Geometric Configuration of Riemannian Submanifolds of arbitrary Codimension

Mohamed Abdelmalek·Mohammed Benalili·Kamil Niedziałomski
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Abstract

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.

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Mohamed Abdelmalek, Mohammed Benalili, Kamil Niedziałomski. 2016-05-12. Geometric Configuration of Riemannian Submanifolds of arbitrary Codimension. https://arxiv.org/abs/1605.03875

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