Results 21 to 30 of about 658 (33)

Geodesic knots in cusped hyperbolic 3-manifolds

, 2009
We consider the existence of simple closed geodesics or "geodesic knots" in finite volume orientable hyperbolic 3-manifolds. Previous results show that at least one geodesic knot always exists [Bull. London Math. Soc.
Chinburg, Miller, Sakai, Sally M Kuhlmann   +3 more
core   +1 more source

An approach for minimal surface family passing a curve

, 2014
We investigate minimal surfaces passing a given curve in $R^{3}$. Using the Frenet frame of a given curve and isothermal parameter, we derive the necessary and sufficient condition for minimal surface.
Kahyaoğlu, Sedat, Kasap, Emin
core   +1 more source

Riemannian and Sub-Riemannian geodesic flows

, 2015
In the present paper we show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This helps us to describe the geodesic flow of
Grong, Erlend, Molina, Mauricio Godoy
core   +1 more source

A note on multi-dimensional Camassa-Holm type systems on the torus

, 2012
We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\
Arnold V I, Constantin A, Freed D, Gay-Balmaz F, Guha P, Holm D D, Holm D D, Hunter J K, Kohlmann M, Liu J Yin Z, Liu J Yin Z, Martin Kohlmann, McKean H P, Wu H, Zou D   +14 more
core   +1 more source

Configurations of curves and geodesics on surfaces

, 1999
We study configurations of immersed curves in surfaces and surfaces in 3-manifolds. Among other results, we show that primitive curves have only finitely many configurations which minimize the number of double points.
Hass, Joel, Scott, Peter
core   +1 more source

Isometric action of SL(2,R) on homogeneous spaces

, 2009
We investigate the SL(2,R) invariant geodesic curves with the as- sociated invariant distance function in parabolic geometry. Parabolic geom- etry naturally occurs in the study of SL(2,R) and is placed in between the elliptic and the hyperbolic (also ...
Kisil, Anastasia V.
core   +1 more source

Focal Rigidity of Flat Tori [PDF]

, 2011
Given a closed Riemannian manifold (M, g), there is a partition \Sigma_i of its tangent bundle TM called the focal decomposition. The sets \Sigma_i are closely associated to focusing of geodesics of (M, g), i.e. to the situation where there are exactly i
Kwakkel, Ferry, Martens, Marco, Peixoto, Mauricio   +2 more
core   +1 more source

The index of a geodesic in a Randers space and some remarks about the lack of regularity of the energy functional of a Finsler metric

, 2010
In some recent papers, the relations existing between the metric properties of Randers spaces and the conformal geometry of stationary Lorentzian manifolds were discovered and investigated.
Caponio, Erasmo
core  

The reach, metric distortion, geodesic convexity and the variation of tangent spaces. [PDF]

J Appl Comput Topol, 2019
Boissonnat JD, Lieutier A, Wintraecken M.   +2 more
europepmc   +1 more source

Orexin/hypocretin and histamine: distinct roles in the control of wakefulness demonstrated using knock-out mouse models. [PDF]

J Neurosci, 2009
Anaclet C, Parmentier R, Ouk K, Guidon G, Buda C, Sastre JP, Akaoka H, Sergeeva OA, Yanagisawa M, Ohtsu H, Franco P, Haas HL, Lin JS.   +12 more
europepmc   +1 more source