60 citations · 137 across the 27 of their papers we have counts for
30 papers
A Novel Geometric Realization of the Yajima-Oikawa Equations
Annalisa Calini, Thomas A. Ivey
We show that the Yajima-Oikawa (YO) equations, a model of short wave-long wave interaction, arise from a simple geometric flow on curves in the 3-dimensional sphere that are…
mKdV-Related Flows for Legendrian Curves in the Pseudohermitian 3-Sphere
Annalisa Calini, Thomas Ivey, Emilio Musso
We investigate geometric evolution equations for Legendrian curves in the 3-sphere which are invariant under the action of the unitary group . We define a natural sympl…
Introducing the Classical Method of Moving Frames
Thomas A. Ivey
The method of moving frames (repère mobile) was used by Elie Cartan as a way of organizing the identification of differential invariants and solving equivalence problems. In this e…
Twisted-Austere Submanifolds in Euclidean Space
Thomas A. Ivey, Spiro Karigiannis
A twisted-austere -fold in consists of a -dimensional submanifold of together with a closed -form on such that the `twiste…
Integrable Geometric Flows for Curves in the Pseudoconformal 3-Sphere
Annalisa Calini, Thomas Ivey
We consider evolution equations for curves in the 3-dimensional sphere that are invariant under the group of pseudoconformal transformations, which preserves the st…
Isometric Embedding for Surfaces: Classical Approaches and Integrability
Thomas A. Ivey
We review classical approaches to the problem of isometrically embedding a Riemannian surface into Euclidean 3-space, including coordinate-based approaches exposited by Darboux and…