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Publications Influence

Ricci solitons on compact three-manifolds

- Thomas A. Ivey
- Mathematics
- 1 December 1993

Abstract In this short article we show that there are no compact three-dimensional Ricci solitons other than spaces of constant curvature. This generalizes a result obtained for surfaces by Hamilton… Expand

262 24- PDF

Cartan for beginners

- Thomas A. Ivey, J. Landsberg
- Mathematics
- 2003

Moving frames and exterior differential systems Euclidean geometry and Riemannian geometry Projective geometry Cartan-Kahler I: Linear algebra and constant-coefficient homogeneous systems… Expand

197 9

Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems, Second Edition

- Thomas A. Ivey, J. Landsberg
- Mathematics
- 15 December 2016

p. 17, Def. 1.6.4, line 2 change ω|e to ωe p. 17, line -1 change Ada−1 to Ad(a −1) p. 18, Def. 1.6.9 right-hand side of displayed equation should read [ω(X), θ(Y )] − [ω(Y ), θ(X)] (not +) p. 19,… Expand

86 7- PDF

Moving frames and exterior differential systems

- Thomas A. Ivey, J. Landsberg
- Mathematics
- 23 September 2003

75 6

BÄCKLUND TRANSFORMATIONS AND KNOTS OF CONSTANT TORSION

- A. Calini, Thomas A. Ivey
- Mathematics
- 7 August 1996

The Backlund transformation for pseudospherical surfaces, which is equivalent to that of the sine-Gordon equation, can be restricted to give a transformation on space curves that preserves constant… Expand

52 4- PDF

New examples of complete Ricci solitons

- Thomas A. Ivey
- Physics
- 1994

The Ricci soliton condition reduces to a set of ODEs when one assumes that the metric is a doubly-warped product of a ray with a sphere and an Einstein manifold. If the Einstein manifold has positive… Expand

77 4- PDF

Hopf Hypersurfaces of Small Hopf Principal Curvature in CH^2

- Thomas A. Ivey, P. Ryan
- Mathematics
- 24 December 2008

Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space CH^2 with any specified value of the Hopf principal… Expand

25 4- PDF

Knot Types, Homotopies and Stability of Closed Elastic Rods

- Thomas A. Ivey, D. A. Singer
- Mathematics
- 28 January 1999

The energy minimization problem associated to uniform, isotropic, linearly elastic rods leads to a geometric variational problem for the rod centerline, whose solutions include closed, knotted… Expand

59 3- PDF

A d’Alembert Formula for Hopf Hypersurfaces

- Thomas A. Ivey
- Mathematics
- 3 December 2009

A Hopf hypersurface in complex hyperbolic space $${\mathbb{C}{\rm H}^n}$$ is one for which the complex structure applied to the normal vector is a principal direction at each point. In this paper,… Expand

9 3- PDF

Remarks on KdV-type flows on star-shaped curves

- A. Calini, Thomas A. Ivey, G. M. Beffa
- Mathematics, Physics
- 26 August 2008

Abstract We study the relation between the centro-affine geometry of star-shaped planar curves and the projective geometry of parametrized maps into R P 1 . We show that projectivization induces a… Expand

33 2- PDF

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