Hyper-complex four-manifolds from the Tzitzéica equation

Abstract

It is shown how solutions to the Tzitzéica equation can be used to construct a family of (pseudo) hyper-complex metrics in four dimensions.

To be published in J.Math.Phys

References in corpus (3)

• The Twisted Photon Associated to Hyper-Hermitian Four-Manifolds
• Hypercomplex Integrable Systems
• From 2D Integrable Systems to Self-Dual Gravity

Cited by in corpus (11)

• Noncommutative Ward's Conjecture and Integrable Systems
• Abelian vortices from Sinh--Gordon and Tzitzeica equations
• Strominger--Yau--Zaslow geometry, Affine Spheres and Painlevé III
• Pseudo-hyperkahler Geometry and Generalized Kahler Geometry
• On paraquaternionic submersions between paraquaternionic Kähler manifolds
• Hyper-ParaHermitian manifolds with torsion
• Some constructions of almost para-hyperhermitian structures on manifolds and tangent bundles
• Geometry of Paraquaternionic Kahler manifolds with torsion
• A dispersionless integrable system associated to Diff$(S^1)$ gauge theory
• Tzitzéica transformation is a dressing action
• Rank 2 Bäcklund Transformations of Hyperbolic Monge-Ampère Systems