A Discrete Representation of the Second Fundamental Form

Carriazo, Alfonso; Fernández, Luis M.; Ramírez-de-Arellano, Antonio

doi:10.3390/math10132279

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Article

29 June 2022

10 Pages

A Discrete Representation of the Second Fundamental Form

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Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, C./Tarfia, s.n., 41012 Sevilla, Spain

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Mathematics2022, 10(13), 2279;https://doi.org/10.3390/math10132279

This article belongs to the Special Issue Geometry of Manifolds and Applications

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Abstract

We present a new method to obtain a combinatorial representation for the behaviour of a submanifold isometrically immersed in a Riemannian manifold based on the second fundamental form. We also present several results applying this new way of representation.

Keywords:

geometry of submanifolds; combinatorial structure; second fundamental form; totally umbilical submanifold; minimal submanifold; Lagrangian submanifold

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