College of Natural & Agricultural Sciences

Skye 284 / Zoom

Gueo Grantcharov, Florida International University

In a 4-dimensional vector space with metric of signature (2,2), two isotropic vectors spanning an isotropic plane determine a canonical action of the split quaternions and the resulting structure is called para-hypercomplex. We use this fact to notice that on an oriented 4-manifold with two isotropic Killing vector fields spanning an isotropic plane everywhere, the induced almost para-hypercomplex structure is integrable. Based on the classification of compact complex surfaces this fact allows us to describe the topology of the compact 4-manifolds with such vector fields. In the talk I’ll discuss the relation of the result with other geometric properties of split-signature 4-manifolds as well as present examples of para-hyperhermitian structures admitting 2 null Killing vector fields.

Contact Information
Qi Zhang
Target Audience
General Public
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