Gideon Maschler, Clark University
Title: Distinguished Kähler metrics and shear operators
Abstract:
We give an outline of an explicit construction, or alternatively
a proof of existence, for a number of
distinguished Kähler metrics.
These include complete Kähler-Einstein metrics and Kähler-Ricci
solitons
of cohomogeneity one under the action of a unimodular group
such as the
Heisenberg
group H2n+1, n ≥ 1 or the 3-dimensional
group of plane Euclidean
motions E(2). We will also describe how these
metrics derive from an ansatz
that originated from a recasting of the
Newlander-Nirenberg complex structure
integrability in terms of so-called
shear operators.
This is joint work with Robert Ream.