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Natural Curvature Conditions

  • Johan GielisEmail author
Chapter

Abstract

Curvature, in all of its aspects is at the core of geometry. Going straight is central to geometry, but it is also a fiction, since we live in a curved world with gravitational attraction in landscapes of mountains, valleys and planes. Nevertheless it is a very useful fiction, and the basis of Euclidean geometry and our science. How then to define being curved, intrinsically and/or as a deviation from planarity? This is one of the central questions in mathematics and geometry; we have derived Euclidean geometry, one geometry that is in accordance with our intuition and our position on earth (with its gravitational field).

Keywords

Sectional Curvature Gaussian Curvature Principal Curvature Chebyshev Polynomial Euclidean Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Atlantis Press and the author(s) 2017

Authors and Affiliations

  1. 1.Department of Biosciences EngineeringUniversity of AntwerpAntwerpBelgium

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