Real hypersurfaces in unimodular complex surfaces
Abstract
A unimodular complex surface is a complex 2-manifold X endowed with a holomorphic
volume form. A strictly pseudoconvex real hypersurface M in X inherits not only a
CR-structure but a canonical coframing as well. In this article, this canonical coframing
on M is defined, its invariants are discussed and interpreted geometrically, and its
basic properties are studied. A natural evolution equation for strictly pseudoconvex
real hypersurfaces in unimodular complex surfaces is defined, some of its properties
are discussed, and several examples are computed. The locally homogeneous examples
are determined and used to illustrate various features of the geometry of the induced
structure on the hypersurface.
Type
Journal articlePermalink
https://hdl.handle.net/10161/13136Collections
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Show full item recordScholars@Duke
Robert Bryant
Phillip Griffiths Professor of Mathematics
My research concerns problems in the geometric theory of partial differential equations.
More specifically, I work on conservation laws for PDE, Finsler geometry, projective
geometry, and Riemannian geometry, including calibrations and the theory of holonomy.
Much of my work involves or develops techniques for studying systems of partial differential
equations that arise in geometric problems. Because of their built-in invariance
properties, these systems often have specia
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