A Discrete Representation of the Second Fundamental Form

Alfonso Carriazo, Luis M. Fernández and Antonio Ramírez- de-Arellano
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Alfonso Carriazo: Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, C./Tarfia, s.n., 41012 Sevilla, Spain
Luis M. Fernández: Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, C./Tarfia, s.n., 41012 Sevilla, Spain
Antonio Ramírez- de-Arellano: Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, C./Tarfia, s.n., 41012 Sevilla, Spain

Mathematics, 2022, vol. 10, issue 13, 1-10

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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