Publication
Equivariant gluing constructions of contact-stationary Legendrian submanifolds in the (2n+1)-sphere
AbstractA contact-stationary Legendrian submanifold of the (2n+1)-sphere is a Legendrian submanifold whose volume is stationary under contact deformations. The simplest contact-stationary Legendrian submanifold (actually minimal Legendrian) is the real, equatorial n-sphere S_0. This paper develops a method for constructing contact-stationary (but not minimal) Legendrian submanifolds of the (2n+1)-sphere by gluing together configurations of sufficiently many U(n + 1)-rotated copies of S_0. Two examples of the construction, corresponding to finite cyclic subgroups of U(n+1), are given. The resulting submanifolds are very symmetric; are geometrically akin to a ‘necklace’ of copies of S_0 attached to each other by narrow necks and winding a large number of times around the (2n+1)-sphere before closing up on themselves; and are topologically equivalent to the product of a circle with the (n-1)-sphere.
Download publicationRelated Resources
See what’s new.
2025
Jet Engine Efficiency takes off at the Autodesk GallerySee how an Autodesk Research project aimed at making more efficient…
2009
Should the Neural–mechanical Behaviour of a Muscle be Coupled or Co-vary?To produce a torque about a joint in the human body there must be…
2012
Programming and Controlling Self-Folding RobotsThis paper describes a robot in the form of a self-folding sheet that…
2016
Energy-Brushes: Interactive Tools for Illustrating Stylized Elemental DynamicsDynamic effects such as waves, splashes, fire, smoke, and explosions…
Get in touch
Something pique your interest? Get in touch if you’d like to learn more about Autodesk Research, our projects, people, and potential collaboration opportunities.
Contact us