Giovanni Russo, Florida International University
"Nearly Kahler metrics and torus symmetry"
Nearly
Kahler
manifolds
are
Riemannian
spaces
equipped
with
an
almost
Hermitian
structure
of
special
type.
In
dimension
six,
nearly
Kahler
metrics
are
Einstein
with
positive
scalar
curvature,
and
have
interesting
connections
with
G2
and
spin
geometry.
At
present
there
are
very
few
compact
examples,
which
are
either
homogeneous
or
of
cohomogeneity
one.
In
this
talk
we
explain
a
theory
of
nearly
Kahler
six-manifolds
admitting
a
two-torus
symmetry.
The
torus-action
yields
a
multi-moment
map,
which
we
use
as
a
Morse
function
to
understand
the
structure
of
the
whole
manifold.
In
particular,
we
show
how
the
local
geometry
of
a
nearly
Kahler
six-manifold
can
be
recovered
from
three-dimensional
data,
and
discuss
connections
with
GKM
theory.
QNC 2501