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  • Print publication year: 2019
  • Online publication date: October 2019

1 - Geometry of Surfaces in R3

Summary

In this preliminary chapter we study the geometry of smooth two-dimensional surfaces in $\mathbb{R}^3$ as a “warm-up problem” and we recover some classical results. In the fist part of the chapter we consider surfaces in $\mathbb{R}^3$ endowed with the standard Euclidean product. In the second part we study surfaces in the 3D pseudo-Euclidean space, that is $\mathbb{R}^3$ endowed with a sign-indefinite inner product.

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