Conformal, Riemannian and Lagrangian Geometry

2002 ◽  
Keyword(s):  
Lagrangian Geometry

scholarly journals Split Special Lagrangian Geometry

2012 ◽  
pp. 43-89 ◽  
Author(s):  
F. Reese Harvey ◽  
H. Blaine Lawson
Keyword(s):  
Special Lagrangian ◽  
Lagrangian Geometry

scholarly journals Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex

2017 ◽  
Vol 24 (3) ◽  
pp. 379-392 ◽  
Author(s):  
Jezabel Curbelo ◽  
Víctor José García-Garrido ◽  
Carlos Roberto Mechoso ◽  
Ana Maria Mancho ◽  
Stephen Wiggins ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Polar Vortex ◽  
Reanalysis Data ◽  
Strong Mixing ◽  
Mixing Processes ◽  
Stratospheric Polar Vortex ◽  
Vertical Extension ◽  
Antarctic Polar Vortex ◽  
The Antarctic ◽  
Lagrangian Geometry

Abstract. In this paper we study the three-dimensional (3-D) Lagrangian structures in the stratospheric polar vortex (SPV) above Antarctica. We analyse and visualize these structures using Lagrangian descriptor function M. The procedure for calculation with reanalysis data is explained. Benchmarks are computed and analysed that allow us to compare 2-D and 3-D aspects of Lagrangian transport. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied. In order to illustrate our approach we select an interval of time in which the SPV is relatively undisturbed (August 1979) and an interval of rapid SPV changes (October 1979). Our results provide new insights into the Lagrangian structure of the vertical extension of the stratospheric polar vortex and its evolution. Our results also show complex Lagrangian patterns indicative of strong mixing processes in the upper troposphere and lower stratosphere. Finally, during the transition to summer in the late spring, we illustrate the vertical structure of two counterrotating vortices, one the polar and the other an emerging one, and the invariant separatrix that divides them.

scholarly journals Lagrangian geometry of the Gauss images of isoparametric hypersurfaces in spheres

2019 ◽  
Vol 6 (1) ◽  
pp. 265-278
Author(s):  
Reiko Miyaoka ◽  
Yoshihiro Ohnita
Keyword(s):  
Lagrangian Submanifolds ◽  
Joint Work ◽  
Standard Sphere ◽  
Isoparametric Hypersurfaces ◽  
Survey Article ◽  
Complex Hyperquadric ◽  
Hypersurfaces In Spheres ◽  
Lagrangian Geometry

AbstractThe Gauss images of isoparametric hypersufaces of the standard sphere Sn+1 provide a rich class of compact minimal Lagrangian submanifolds embedded in the complex hyperquadric Qn(ℂ). This is a survey article based on our joint work [17] to study the Hamiltonian non-displaceability and related properties of such Lagrangian submanifolds.

Supplementary material to "Insights on the three-dimensional Lagrangian geometry of the Antarctic Polar Vortex"

2017 ◽  
Author(s):  
Jezabel Curbelo ◽  
Victor J. García-Garrido ◽  
Carlos R. Mechoso ◽  
Ana M. Mancho ◽  
Stephen Wiggins ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Polar Vortex ◽  
Supplementary Material ◽  
Antarctic Polar Vortex ◽  
The Antarctic ◽  
Lagrangian Geometry
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