Thomas A. Ivey

works on

constant mean curvature 1 darboux integrability 1 elliptic liouville equation 1 group theory 1 hyperbolic 3-space 1 partial differential equations 1

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math.DG2026

On the Darboux Integrability of the Constant Mean Curvature One Equation for Surfaces in Hyperbolic 3 space

Mark E. Fels, Thomas A. Ivey

The paper proves that the elliptic PDE system governing constant mean curvature one immersions in hyperbolic 3‑space is Darboux integrable and equivalent to the elliptic Liouville…

math.DG2026

Cohomogeneity-One Ruled Hypersurfaces in $CP^{2}$ and $C H^{2}$

Thomas A. Ivey, Patrick J. Ryan

In this paper, we show how to construct a special class of ruled hypersurfaces in the nonflat complex space forms $CP^{n}$ and $C H^{n}$ . This is done by taking an arb…

math.DG2026

The Geometry of Darboux Integrable Elliptic Systems

Mark E. Fels, Thomas A. Ivey

We characterize real elliptic differential systems whose solutions can be expressed in terms of holomorphic solutions to an associated holomorphic Pfaffian system $H$ on a…

math.DG2024

Cohomogeneity one solitons for the isometric flow of $G_{2}$ -structures

Thomas A. Ivey, Spiro Karigiannis

We consider the existence of cohomogeneity one solitons for the isometric flow of $G_{2}$ -structures on the following classes of torsion-free $G_{2}$ -manifolds: the Euclidean $R^{7}$ wit…

On the Darboux Integrability of the Constant Mean Curvature One Equation for Surfaces in Hyperbolic 3 space

Cohomogeneity-One Ruled Hypersurfaces in CP2 and CH2

The Geometry of Darboux Integrable Elliptic Systems

Cohomogeneity one solitons for the isometric flow of G2​-structures

Cohomogeneity-One Ruled Hypersurfaces in $CP^{2}$ and $C H^{2}$

Cohomogeneity one solitons for the isometric flow of $G_{2}$ -structures