Lectures on Closed Geodesics is popular PDF and ePub book, written by W. Klingenberg in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Lectures on Closed Geodesics can be Read Online from any device for your convenience.
Lectures on Closed Geodesics Book PDF Summary
The question of existence of c10sed geodesics on a Riemannian manifold and the properties of the corresponding periodic orbits in the geodesic flow has been the object of intensive investigations since the beginning of global differential geo metry during the last century. The simplest case occurs for c10sed surfaces of negative curvature. Here, the fundamental group is very large and, as shown by Hadamard [Had] in 1898, every non-null homotopic c10sed curve can be deformed into a c10sed curve having minimallength in its free homotopy c1ass. This minimal curve is, up to the parameterization, uniquely determined and represents a c10sed geodesic. The question of existence of a c10sed geodesic on a simply connected c10sed surface is much more difficult. As pointed out by Poincare [po 1] in 1905, this problem has much in common with the problem ofthe existence of periodic orbits in the restricted three body problem. Poincare [l.c.] outlined a proof that on an analytic convex surface which does not differ too much from the standard sphere there always exists at least one c10sed geodesic of elliptic type, i. e., the corres ponding periodic orbit in the geodesic flow is infinitesimally stable.
Detail Book of Lectures on Closed Geodesics PDF
- Author : W. Klingenberg
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9783642618819
- Genre : Mathematics
- Total Page : 238 pages
- Language : English
- PDF File Size : 11,6 Mb
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