Thomas Ivey: Publications

Books & Chapters

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)
 
Ricci Solitons (book chapter co-authored with Ben Chow),
pp. 1–53 in  “The Ricci Flow, Volume 2: Techniques and Applications”,
Mathematical Surveys and Monographs vol. 135, American Mathematical Society, 2007.

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
Proc. A.M.S. 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
Proc. A.M.S. 125 (1997) #4, 1203-1208

On Isometric and Minimal Isometric Embeddings (with J.M. Landsberg)
Duke Math. Journal 89 (1997), 555-576.  (arXiv link)

Bäcklund transformations and knots of constant torsion (with A. Calini)
Journal of Knot Theory and its Ramifications, 7 #6 (1998), 719-746
(arXiv link; 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 (arXiv link)

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

Minimal Curves of Constant Torsion
Proc. A.M.S. 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)
- Trans. Amer. Math. Soc. 357 (2005), 1061–1093.  (arXiv link)

Finite-gap solutions of the vortex filament equation:
symmetric solutions and genus one solutions
(with A. Calini)
J. Nonlin. Sci. 15 (2005), 321–361.

Geometry and Topology of Finite-Gap Vortex Filaments
pp. 187–202 in Proceedings of the Seventh International Conference on Geometry,
 Integrablility and Quantization (Varna, 2005), Bulgarian Academy of Sciences, 2006.

Finite-gap solutions of the vortex filament equation: Isoperiodic Deformations (with A. Calini)
J. Nonlin. Sci 17 (2007), 527-567.

Spectral stability analysis for periodic traveling wave solutions of NLS and CGL perturbations (with S. Lafortune)
Physica D 237 (2008), 1750-1772.

Bäcklund Transformations and Darboux Integrability for Nonlinear Wave Equations (with J. Clelland)
Asian J. Math. 13 (2009), 13-64. (arXiv link)

Hopf Hypersurfaces of Small Hopf Principal Curvature in CH2 (with P.J. Ryan)
Geometriae Dedicata 141 (2009), 147-161. (arXiv link)

Remarks on KdV-type Flows on Star-Shaped Curves
(with A. Calini and G. Marí Beffa)
Physica D 238 (2009), 788--797.  (arXiv link)

Symmetric Pseudospherical Surfaces I: General Theory
(with J. Dorfmeister and I. Sterling)
Results in Mathematics 56 (2009), 3--21.  (arXiv link)

The structure Jacobi operator for hypersurfaces in
CP2 and CH2 (with P.J. Ryan)
Results in Mathematics 56 (2009), 473-488. (arXiv link)

Austere Submanifolds of Dimension Four: Examples and Maximal Types
(with M. Ionel)
to appear in Illinois J. Math.  (arXiv link)

In Preparation

The Ricci-* Tensor for Hypersurfaces in
CPn and CHn (with P.J. Ryan)
submitted to Tokyo J. Math.

Ruled Austere Submanifolds of Dimension Four
(with M. Ionel)
 
An Integrable Flow for Starlike Curves in Centroaffine Space
(with A. Calini and G. Marí Beffa)