Abstract:
In a joint work with J. Davidov, O. Mushkarov and M. Yotov
we considered some geometric structures on compact complex surfaces
that are related to split quaternions and lead to existence of
indefinite anti-selfdual metrics. These structures, called
para-hypercomplex, para-hyperhermitian and para-hyperkähler (or
hypersymplectic) , are analogs of the hypercomplex, hyperhermitian
and hyperkähler structures in the definite case. Every compact
complex surface admitting a para-hyperhermitian structure has
vanishing first Chern class and, unlike the definite case, many of
these surfaces carry infinite dimensional families of such
structures. In the talk will be explained the relation among the
different structures together with several examples and some open
problems.
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