Lecture

Geodesic Curves: Minimizing Distance and Constant Speed

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In course

MATH-213: Differential geometry I - curves and surfaces

This course serves as an introduction to classical differential geometry, which studies the geometric properties of curves and surfaces in the Euclidean space. ...

Description

This lecture discusses geodesic curves parameterized at constant speed to minimize the distance between two points. The instructor explains the concept of geodesic curves and their properties, such as minimizing distances and being parameterized at constant speed. The lecture covers the theorem related to geodesic curves and their behavior when minimizing distances. It also delves into the concept of geodesic rest and the conditions under which a curve is considered geodesic. The lecture concludes with a discussion on the normal curvature of regular curves and their geodesic properties.

Instructor

Marc Troyanov

Expertise Differential Geometry Geometric Analysis Teaching & PhD Past EPFL PhD Students Olivier Mermoud, Khaled Gafaiti, Serguei Timochine, Stephen Ducret, Ratiba Djelid, Zahra Sinaei, Luc Genton, Adrien Giuliano Marcone, Guillaume Buro, Bruno Luiz Santos Correia Courses Advanced linear algebra II MATH-115(b) The purpose of this course is to introduce some basic notions of linear algebra and to rigorously prove the main results in the field.

Official source

Ontological neighbourhood

Mathematics

Geometry: Euclidean geometry, Differential geometry

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