WebBUMPY METRICS R. ABRAHAM On a compact Riemannian manifold, M, there ought to be infinitely many geodesics (a classical conjecture). This is obvious if the isometry group of M has dimension greater than zero, so we should examine the "generic case" of minimal symmetry. For example, suppose M is a 2-sphere embedded in 3-space, with the metric. WebHowever, the Bumpy Metric Theorem proven by Abraham [3] in 1970 states that for generic choice of Riemannian metric, all nonconstant smooth closed geodesics lie on nondegenerate critical submanifolds of dimension one, and have the property that their only Jacobi fields are those generated by the S1-action.
Bumpy Riemannian Metrics and Closed Parametrized …
WebBumpy Metrics Theorem for Geodesic Nets Bruno Staffa Subjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP); Metric Geometry (math.MG) [8] arXiv:2203.00651 (replaced) [ pdf, other] Gaussian Zonoids, Gaussian determinants and Gaussian random fields Léo Mathis Comments: Major changes. An error was spoted and corrected. WebOct 23, 2024 · In analogy with the classical result for nondegenerate closed geodesics, we will call such metrics (M,\Sigma ) - bumpy metrics. This result is analogous to a similar result for closed geodesics, obtained by Abraham [ 1] and Anosov [ 4] which are related to properties of geodesic flows for generic Riemannian metrics on a closed smooth manifold. island park whiskey
JOHN DOUGLAS MOORE - JSTOR
WebBumpy Metrics. Ralph Abraham. We prove that on a compact manifold, almost all metrics are bumpy. WebDefine bumpy. bumpy synonyms, bumpy pronunciation, bumpy translation, English dictionary definition of bumpy. adj. bump·i·er , bump·i·est 1. Covered with or full of … WebThe first step needed is a bumpy metric theorem which states that when a Riemannian manifold has a generic metric, all prime minimal surfaces are free of branch points and … keyter catalogo