A Discrete Representation of the Second Fundamental Form

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.

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 13; p. 2279
Main Authors Carriazo, Alfonso, Fernández, Luis M., Ramírez-de-Arellano, Antonio
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2022
Subjects
Combinatorial analysis
combinatorial structure
Food science
Geometry
geometry of submanifolds
Lagrangian submanifold
Manifolds (mathematics)
minimal submanifold
Representations
Riemann manifold
second fundamental form
totally umbilical submanifold
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10132279