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Quadratic integrals of geodesic flow, webs, and integrable billiards
(2021-03-01)
We present a geometric interpretation of integrability of geodesic flow by quadratic integrals in terms of the web theory and construct integrable billiards on surfaces admitting such integrals.
The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
(de Gruyter, 2013-10)
Let Sk,m be the pseudosphere of signature (k,m). We show that the space ℒ0(Sk,m) of all oriented null geodesics in Sk,m is a manifold, and we describe geometrically its canonical contact distribution in terms of the space ...
The magnetic flow on the manifold of oriented geodesics of a three dimensional space form
(Osaka University. Departments of Mathematics, 2013-09)
Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0,10,1 or −1−1. Let L be the manifold of all (unparametrized) complete oriented geodesics of M, endowed with its canonical ...
Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals
(INDIANA UNIV MATH JOURNAL, 2009)
We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical ...
Rotation effect on geodesic and zonal flow modes in tokamak plasmas with isothermal magnetic surfaces
(IOP PUBLISHING LTD, 2011)
The electrostatic geodesic mode oscillations are investigated in rotating large aspect ratio tokamak plasmas with circular isothermal magnetic surfaces. The analysis is carried out within the magnetohydrodynamic model ...
On first integrals of the geodesic flow on Heisenberg nilmanifolds
(Elsevier Science, 2016-12)
In this paper we study the geodesic flow on nilmanifolds equipped with a left-invariant metric. We write the underlying definitions and find general formulas for the Poisson involution. As an application we develop the ...
The geodesic flow on nilpotent lie groups of steps two and three
(American Institute of Mathematical Sciences, 2021-09)
The goal of this paper is the study of the integrability of the geodesic flow on k-step nilpotent Lie groups, k=2,3, when equipped with a leftinvariant metric. Liouville integrability is proved in low dimensions. Moreover, ...
GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS
(JULIUSZ SCHAUDER CTR NONLINEAR STUDIES, 2010)
Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable ...
On a formula for the spectral flow and its applications
(WILEY-V C H VERLAG GMBH, 2010)
We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of ...