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 very old DVI file, in which some fonts have been converted incorrectly, and unfortunately the figures are no longer viewable.]

Papers  (click on titles to download reprints in PDF format)

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)

Hypersurfaces with Codazzi-type shape operator for a Tanaka-Webster connection 
(with P.J. Ryan), Publ. Math. Debrecen 87 #3-4 (2015), 279–290.  (pdf)

Hypersurfaces in CP2 and CH2 with Two Distinct Principal Curvatures (with P.J. Ryan), Glasgow Math. J. 58 (2015), 137–152. (arXiv link)

Austere Submanifolds in Complex Projective Space (with M. Ionel), Comm. Anal. Geom. 24 (2016), 821–841.   (arXiv link)

Stark Hypersurfaces in Complex Projective Space, Contemporary Mathematics 674 (2016), 75–88. (arXiv link)

Stability of closed solutions to the VFE hierarchy and application to the Hirota equation (with S. Lafortune), Nonlinearity 31 (2018), 458–490.  (arXiv link)

Reflections on the Geometry of Chords, in Mathematical Music Theory, World Scientific, 2018.  (publisher's page)

Geometric characterization and classification of Bäcklund Transformations of sine- Gordon type (with J. Clelland), J. Integrable Systems 3 (2018), 1–44.  (arXiv link)

Darboux-Integrable Isometric Embeddings of Surfaces (with J. Clelland, N. Tehseen and P. Vassiliou), Geometriae Dedicata 203 (2019), 353–388. (arXiv link)

Isometric Embedding for Surfaces: Classical Approaches and Integrability, to appear in Contemporary Mathematics (arXiv link)

In Preparation

Remarks on Twisted-Austere Submanifolds (with S. Karigiannis), submitted to Geometriae Dedicata.  (arXiv link)

Integrable Evolution Equations for Curves in the Pseudoconformal 3-sphere, with A. Calini

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