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Two-forms on four-manifolds and elliptic equations

· 2006 · math.DG · arXiv math/0607083

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abstract

We define a general class of elliptic equations for 2-forms on 4-manifolds, of which the complex Monge-Ampere equation is a prototype. We obtain some regularity results and discuss various connections (some speculative) with modern symplectic 4-manifold theory.

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math.DG 1

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2024 1

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Four-dimensional Riemannian geometry via 2-forms

math.DG · 2024-05-24 · unverdicted · novelty 7.0

A description of 4D Riemannian geometry via 2-forms valued in an SO(3) bundle from SU(2)-structures, yielding a unique invariant functional with Einstein critical points.

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  • Four-dimensional Riemannian geometry via 2-forms math.DG · 2024-05-24 · unverdicted · none · ref 12 · internal anchor

    A description of 4D Riemannian geometry via 2-forms valued in an SO(3) bundle from SU(2)-structures, yielding a unique invariant functional with Einstein critical points.