79 research outputs found
Entire invariant solutions to Monge-Ampere equations
We prove existence and regularity of entire solutions to Monge-Ampere
equations invariant under an irreducible action of a compact Lie group.Comment: version 2: 4 pages; a reference added; other minor changes; to appear
in Proc. AM
Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action
We classify those manifolds mentioned in the title which have finite
topological type. Namely we show any such connected M is isomorphic to a
hyperkaehler quotient of a flat quaternionic vector space by an abelian group.
We also show that a compact connected and simply connected 3-Sasakian
manifold of dimension 4n-1 whose isometry group has rank n+1 is isometric to a
3-Sasakian quotient of a sphere by a torus. As a corollary, a compact connected
quaternion-Kaehler 4n-manifold with positive scalar curvature and isometry
group of rank n+1 is isometric to the quaternionic projective space or the
complex grassmanian.Comment: 18 pages, AMS-Latex, replaced with a final version (minor
corrections) on 14.01.1999; to appear in Math. An
Prescribing Ricci curvature on complexified symmetric spaces
In this note we show that any real exact G-invariant (1,1)-form is the Ricci
form of a Kaehler metric on the complexification of an irreducible compact
symmetric space G/K.Comment: 6 pages; arguments expanded, details filled i
Complexification and hypercomplexification of manifolds with a linear connection
We give a simple interpretation of the adapted complex structure of
Lempert-Szoke and Guillemin-Stenzel: it is given by a polar decomposition of
the complexified manifold. We then give a twistorial construction of an
SO(3)-invariant hypercomplex structure on a neighbourhood of in ,
where is a real-analytic manifold equipped with a linear connection. We
show that the Nahm equations arise naturally in this context: for a connection
with zero curvature and arbitrary torsion, the real sections of the twistor
space can be obtained by solving Nahm's equations in the Lie algebra of certain
vector fields. Finally, we show that, if we start with a metric connection,
then our construction yields an SO(3)-invariant hyperk\"ahler metric.Comment: some corrections, a reference added, to appear in International J. of
Mathematic
Asymptotic metrics for SU(N)-monopoles with maximal symmetry breaking
We compute the asymptotic metrics for moduli spaces of SU(N) monopoles with
maximal symmetry breaking. These metrics are exponentially close to the exact
monopole metric as soon as, for each simple root, the individual monopoles
corresponding to that root are well separated. We also show that the estimates
can be differentiated term by term in natural coordinates, which is a new
result even for SU(2) monopoles.Comment: 26 pages, AMS-Latex; comparison of metrics done differently and in
greater detail; version submitte
Hyperk\"ahler Manifolds of Curves in Twistor Spaces
We discuss hypercomplex and hyperk\"ahler structures obtained from higher
degree curves in complex spaces fibring over .Comment: v4: added the missing assumption on dimension in Theorem 3.1
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