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 in:Mathematics (Basel) 2022-07, Vol.10 (13), p.2279
Main Authors: Carriazo, Alfonso, Fernández, Luis M., Ramírez-de-Arellano, Antonio
Format: Article
Language:English
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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Description
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