Thomas Ivey: Publications

Books

Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems
(with J.M. Landsberg),
Graduate Studies in Mathematics Vol. 61, American Mathematical Society, 2003.
(ISBN: 0-8218-3375-8)
 

Thesis

On Solitons for the Ricci Flow (Duke University, 1992)
   [This is a PDF version of a very old DVI file, in which some fonts have been converted incorrectly, and figures are no longer viewable.]

Papers

(click on titles to download reprints in PDF format; these are readable with Acrobat Reader, available for free here)

Ricci solitons on compact three-manifolds
-Differential Geometry and its Applications, 3 (1993) 301-307.

New Examples of Complete Ricci Solitons
- AMS Proceedings 122 (1994) #1, 241-246.

The Ricci Flow on Radially Symmetric R3
-Communications in Partial Differential Equations, 19 (1994) #9/10, 1481-1500.

Surfaces with orthogonal families of circles
- AMS Proceedings 123 (1995) #3, 865-872.

Affine Isometric Embeddings and Rigidity
-Geometriae Dedicata, 64 (1997), 125-144.

Local Existence of Ricci Solitons
- Manuscripta Mathematica 91 (1996), 151-162.

Ricci solitons on compact Kähler surfaces
- AMS Proceedings 125 (1997) #4, 1203-1208

On Isometric and Minimal Isometric Embeddings (with J.M. Landsberg)
- Duke Math. Journal 89 (1997), 555-576
(go here for abstract, TeX source & postscript)

Bäcklund transformations and knots of constant torsion (with A. Calini)
- Journal of Knot Theory and its Ramifications, 7 #6 (1998), 719-746
(go here for abstract, TeX source & postscript of an earlier version;
gzipped postscript file for the final version available here)

Topology of constant torsion curves evolving under the sine-Gordon equation (with A. Calini)
- Phys. Letters A, 254 (1999), 170-178.

Affine isometric embedding for surfaces
- Geometriae Dedicata, 75 (1999), 235-243.

Knot Types, Homotopies and Stability of Elastic Rods (with D. Singer)
- Proc. London Math. Soc.79 (1999) 429--450.
(click here for abstract, LaTeX source & postscript)

Helices, Hasimoto surfaces and Bäcklund transformations
- Canadian Math. Bull. 43 (2000), 427--439.

Minimal Curves of Constant Torsion
- AMS Proceedings 128 (2000), 2095--2103.

Knot types, Floquet spectra, and finite-gap solutions of the Vortex Filament Equation (with A.Calini)
- Mathematics and Computers in Simulation 55 (2001), 341-350.

Connecting geometry, topology and spectra for finite-gap NLS potentials (with A. Calini),
- Physica D, 152/153 (2001), 9--19.

Integrable Geometric Evolution Equations for Curves,
- Contemp. Math. 285 (2001), 71--84.

An inverse problem from sub-Riemannian geometry,
- Pacific Math. J. 208 (2003), 111-124.

Parametric Bäcklund Transformations I: Phenomenology (with J. Clelland)
- Transactions of the AMS, 357 (2005), 1061-1093.

Finite-gap solutions of the vortex filament equation: Symmetric Solutions
and Genus One Solutions
, (with A. Calini), Journal of Nonlinear Science, vol. 15 #5, 321-361.

Geometry and Topology of Finite-Gap Vortex Filaments, in Proceedings of the Seventh International Conference
on Geometry, Integrablility and Quantization (Varna, 2005), Bulgarian Academy of Sciences, Sofia 2006.

In Preparation

Finite-gap solutions of the vortex filament equation: Isoperiodic Deformations
(with A. Calini), submitted to Journal of Nonlinear Science
(click here for abstract, postscript and PDF versions)