A Discrete Representation of the Second Fundamental Form

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