1. Twistorial construction of minimal hypersurfaces
- Author
-
Johann Davidov
- Subjects
Mathematics - Differential Geometry ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,Integrable system ,twistor spaces ,Structure (category theory) ,Hermitian matrix ,Primary 53C28, Secondary 53A10, 49Q05 ,Hypersurface ,Differential Geometry (math.DG) ,minimal hypersurfaces ,Metric (mathematics) ,FOS: Mathematics ,Twistor space ,Mathematics::Differential Geometry ,Department of Analysis, Geometry and Topology ,Mathematics ,Symplectic geometry - Abstract
Every almost Hermitian structure $(g,J)$ on a four-manifold $M$ determines a hypersurface $\Sigma_J$ in the (positive) twistor space of $(M,g)$ consisting of the complex structures anti-commuting with $J$. In this note we find the conditions under which $\Sigma_J$ is minimal with respect to a natural Riemannian metric on the twistor space in the cases when $J$ is integrable or symplectic. Several examples illustrating the obtained results are also discussed., Comment: 16 pages, typos corrected
- Published
- 2014