33,431 research outputs found
Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space
It has been known for some time that there exist essentially different
real forms of the complex affine Kac-Moody algebra of type and that
one can associate of these real forms with certain classes of "integrable
surfaces", such as minimal Lagrangian surfaces in and , as well as definite and indefinite affine spheres in .
In this paper we consider the class of timelike minimal Lagrangian surfaces
in the indefinite complex hyperbolic two-space . We show that
this class of surfaces corresponds to the fifth real form.
Moreover, for each timelike Lagrangian surface in we
define natural Gauss maps into certain homogeneous spaces and prove a Ruh-Vilms
type theorem, characterizing timelike minimal Lagrangian surfaces among all
timelike Lagrangian surfaces in terms of the harmonicity of these Gauss maps.Comment: Typological errors have been fixe
TeV Scale Mirage Mediation and Natural Little SUSY Hierarchy
TeV scale mirage mediation has been proposed as a supersymmetry breaking
scheme reducing the fine tuning for electroweak symmetry breaking in the
minimal supersymmetric extension of the standard model. We discuss a moduli
stabilization set-up for TeV scale mirage mediation which allows an
extra-dimensional interpretation for the origin of supersymmetry breaking and
naturally gives an weak-scale size of the Higgs B-parameter. The set-up
utilizes the holomorphic gauge kinetic functions depending on both the heavy
dilaton and the light volume modulus whose axion partners are assumed to be
periodic fields. We also examine the low energy phenomenology of TeV scale
mirage mediation, particularly the constraints from electroweak symmetry
breaking and FCNC processes.Comment: 44 pages, 14 figures; added references, extended discussions in
section
Global analysis by hidden symmetry
Hidden symmetry of a G'-space X is defined by an extension of the G'-action
on X to that of a group G containing G' as a subgroup. In this setting, we
study the relationship between the three objects:
(A) global analysis on X by using representations of G (hidden symmetry);
(B) global analysis on X by using representations of G';
(C) branching laws of representations of G when restricted to the subgroup
G'.
We explain a trick which transfers results for finite-dimensional
representations in the compact setting to those for infinite-dimensional
representations in the noncompact setting when is -spherical.
Applications to branching problems of unitary representations, and to spectral
analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th
birthda
A loop group method for minimal surfaces in the three-dimensional Heisenberg group
We characterize constant mean curvature surfaces in the three-dimensional
Heisenberg group by a family of flat connections on the trivial bundle \D
\times \GL over a simply connected domain in the complex plane.
In particular for minimal surfaces, we give an immersion formula, the so-called
Sym-formula, and a generalized Weierstrass type representation via the loop
group method.Comment: 40 pages, v2: The argument for branch points has been fixed and the
references have been updated. v3: The argument for canonical examples has
been fixed and the classification for homogeneous surfaces has been added v4:
Some typos are fixed and Remark 5.4 (3) is adde
Minimal surfaces with non-trivial topology in the three-dimensional Heisenberg group
We study symmetric minimal surfaces in the three-dimensional Heisenberg group
using the generalized Weierstrass type representation, the
so-called loop group method. In particular, we will discuss how to construct
minimal surfaces in with non-trivial topology. Moreover, we
will classify equivariant minimal surfaces given by one-parameter subgroups of
the isometry group of .Comment: 49 page
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