Speaker: Gueo Grantcharov, Florida International University

Title: Complex surfaces and indefinite metrics

Abstract: In a 4-dimensional vector space with scalar product of signature (2,2) and fixed orientation, two independent vectors spanning a maximal isotropic (null) plane determine a canonical action of the split-quaternioins. This provides a relation between null vector fields and structures called para-hypercomplex on 4-dimensional pseudo-Riemannian manifolds.

 A para-hypercomplex structure contains in particular a complex structure, so using the Kodaira classification for compact complex surfaces, one can describe the topology of the underlying 4-manifold in the compact case. I'll discuss the general properties of the metrics and provide basic examples.

Founders Building (FO), FO 2.404
800 W. Campbell Road, Richardson, Texas 75080-3021

Natural Sciences & Mathematics
Stephen E. McKeown

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