Geodesics are locally length minimizing, in that any sufficiently small portion is the shortest path between the endpoints of that portion.

Sep 22, 2024 · The discussion centers on the concept of geodesics in the context of general relativity (GR) and how objects follow these paths due to the curvature of spacetime caused by …

Dec 25, 2020 · 5 It is known that geodesics on a cylinder are helical lines (helix). As a special case of a helix--- straight line. But one can take two points so cleverly that you can draw two …

Mar 26, 2020 · In the usual approach, drawing geodesics is defined in terms of parallel transport, but in the special case of the Levi-civita connection, we can use a more intuitive definition of a …

Feb 16, 2012 · But what about an arbitrary curve? Parallel transport around geodesics is a special case and was explained in one of the answers. I guess you missed it. Before you leave us, be …

Nov 12, 2024 · I am trying to better understand how geodesics and connections are related beyond the usual case of Riemannian manifolds. In particular, I am wondering: If every …

Jul 17, 2021 · In general "differential geometry geodesics" are only locally length minimizing; consider on the sphere the path from the north pole to the south pole, and then go a little …

Mark L. Irons' paper The Curvature and Geodesics of the Torus gives a concise overview of the geodesics on the torus: There are five clear-cut families of geodesics. Most of the geodesics …

Oct 11, 2024 · I am reading Do Carmo "Geometry of Curves and Surfaces" and in section 4.4 (Parallel transport. Geodesics) in Example 4 Do Carmo claims without proof that …

Mar 8, 2014 · Geodesics on torus Ask Question Asked 11 years, 10 months ago Modified 3 years, 1 month ago