Hypercomplex Integrable Systems

Details Hypercomplex Integrable Systems Hypercomplex Integrable Systems

1998-08-27

arxiv.org/abs/solv-int/9808019v1

Physics

High Energy Physics

High Energy Physics - Theory

Latex file, 19 pages

Scientific paper

10.1088/0951-7715/12/5/302

In this paper we study hypercomplex manifolds in four dimensions. Rather than using an approach based on differential forms, we develop a dual approach using vector fields. The condition on these vector fields may then be interpreted as Lax equations, exhibiting the integrability properties of such manifolds. A number of different field equations for such hypercomplex manifolds are derived, one of which is in Cauchy-Kovaleskaya form which enables a formal general solution to be given. Various other properties of the field equations and their solutions are studied, such as their symmetry properties and the associated hierarchy of conservation laws.

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