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.
2018
Hybrid Finite Element-Geometric Forming Simulation of Composite Materials
Computer simulations can extensively help engineers to gain a better…
2013
Towards the Development of a Biomechanical Ontology to Support the Initiatives of the Parametric Human Project
The creation of a conceptual schema that symbolically represents the…
2018
Autodesk @ MaRS
Using generative design in architecture to work around work style,…
2022
Missed AU 2022? Watch these sessions from Autodesk Research
Check out the Autodesk Research panels and presentations from Autodesk…
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