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.


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


(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 CP
2 and CH2 (with P.J. Ryan)
Results in Math. 56 (2009), 473-488. (arXiv link)

Austere Submanifolds of Dimension Four: Examples and Maximal Types
(with M. Ionel)
Illinois J. Math. 54 (2010), 713-746.  (arXiv link)

Stability of Small-Amplitude Torus Knot Solutions of the Localized Induction Equation (with A. Calini)
J. Physics A 44 (2011), 335204 (17 pages).

A d'Alembert Formula for Hopf Hypersurfaces, Results in Math. 60 (2011), 293-309. (arXiv link)

The Ricci-* Tensor for Hypersurfaces in CPn and CHn (with P.J. Ryan),
Tokyo J. Math. 34 (2011), 445-471. (arXiv link)

Ruled Austere Submanifolds of Dimension Four (with M. Ionel),
Differential Geometry and its Applications 30 (2012), 588-603. (arXiv link)

Integrable Flows for Starlike Curves in Centroaffine Space (with A. Calini and G. Marí Beffa),
9 (2013) 022, 21 pages. (arXiv link)

In Preparation

Austere Submanifolds in Complex Projective Space (with M. Ionel)

On Bäcklund Transformations of sine-Gordon Type (with J. Clelland)

Hypersurfaces in CP2 and CH2 with Two Distinct Principal Curvatures (with P.J. Ryan)

A new class of ruled real hypersurfaces in CP2 and CH2 (with P.J. Ryan)