| 书目名称 | Lectures on Closed Geodesics | | 编辑 | Wilhelm Klingenberg | | 视频video | | | 丛书名称 | Grundlehren der mathematischen Wissenschaften | | 图书封面 |  | | 描述 | 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 | | 出版日期 | Book 1978 | | 关键词 | Geschlossene Geodätische; Riemannian manifold; Riemannian manifolds; Riemannsche Mannigfaltigkeit; curva | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-61881-9 | | isbn_softcover | 978-3-642-61883-3 | | isbn_ebook | 978-3-642-61881-9Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Sringer-Verlag Berlin Heidelberg 1978 |
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发表于 2025-3-21 17:20:53
