777 research outputs found
Hamiltonian stationary Lagrangian surfaces in Hermitian symmetric spaces
This paper is the third of a series on Hamiltonian stationary Lagrangian
surfaces. We present here the most general theory, valid for any Hermitian
symmetric target space. Using well-chosen moving frame formalism, we show that
the equations are equivalent to an integrable system, generalizing the C^2
subcase analyzed in the first article (arXiv:math.DG/0009202). This system
shares many features with the harmonic map equation of surfaces into symmetric
spaces, allowing us to develop a theory close to Dorfmeister, Pedit and Wu's,
including for instance a Weierstrass-type representation. Notice that this
article encompasses the article mentioned above, although much fewer details
will be given on that particular flat case
A canonical structure on the tangent bundle of a pseudo- or para-K\"ahler manifold
It is a classical fact that the cotangent bundle T^* \M of a differentiable
manifold \M enjoys a canonical symplectic form . If
(\M,\j,g,\omega) is a pseudo-K\"ahler or para-K\"ahler -dimensional
manifold, we prove that the tangent bundle T\M also enjoys a natural
pseudo-K\"ahler or para-K\"ahler structure (\J,\G,\Omega), where is
the pull-back by of and \G is a pseudo-Riemannian metric with
neutral signature . We investigate the curvature properties of the
pair (\J,\G) and prove that: \G is scalar-flat, is not Einstein unless
is flat, has nonpositive (resp.\ nonnegative) Ricci curvature if and only if
has nonpositive (resp.\ nonnegative) Ricci curvature as well, and is
locally conformally flat if and only if and has constant curvature,
or and is flat. We also check that (i) the holomorphic sectional
curvature of (\J,\G) is not constant unless is flat, and (ii) in
case, that \G is never anti-self-dual, unless conformally flat.Comment: Clarified the statements on the cotangent bundle. Corrected various
typo
Ricci curvature on polyhedral surfaces via optimal transportation
The problem of defining correctly geometric objects such as the curvature is
a hard one in discrete geometry. In 2009, Ollivier defined a notion of
curvature applicable to a wide category of measured metric spaces, in
particular to graphs. He named it coarse Ricci curvature because it coincides,
up to some given factor, with the classical Ricci curvature, when the space is
a smooth manifold. Lin, Lu & Yau, Jost & Liu have used and extended this notion
for graphs giving estimates for the curvature and hence the diameter, in terms
of the combinatorics. In this paper, we describe a method for computing the
coarse Ricci curvature and give sharper results, in the specific but crucial
case of polyhedral surfaces
Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. A discrete Lawson correspondence
The main result of this paper is a discrete Lawson correspondence between
discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. This is a
correspondence between two discrete isothermic surfaces. We show that this
correspondence is an isometry in the following sense: it preserves the metric
coefficients introduced previously by Bobenko and Suris for isothermic nets.
Exactly as in the smooth case, this is a correspondence between nets with the
same Lax matrices, and the immersion formulas also coincide with the smooth
case.Comment: 13 page
Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface
Given an oriented Riemannian surface , its tangent bundle
enjoys a natural pseudo-K\"{a}hler structure, that is the combination
of a complex structure \J, a pseudo-metric \G with neutral signature and a
symplectic structure \Om. We give a local classification of those surfaces of
which are both Lagrangian with respect to \Om and minimal with
respect to \G. We first show that if is non-flat, the only such surfaces
are affine normal bundles over geodesics. In the flat case there is, in
contrast, a large set of Lagrangian minimal surfaces, which is described
explicitly. As an application, we show that motions of surfaces in or
induce Hamiltonian motions of their normal congruences, which are
Lagrangian surfaces in or T \H^2 respectively. We relate the area of
the congruence to a second-order functional
on the original surface.Comment: 22 pages, typos corrected, results streamline
Visible-IR Colors and Lightcurve Analysis of Two Bright TNOs: 1999 TC36 and 1998 SN165
We report on observations of two bright Trans-Neptunian Objects (TNOs) - 1999
TC36 and 1998 SN165}- during two observational campaigns, as part of the Meudon
Multicolor Survey of Outer Solar System Objects. V-J color was measured for
1999 TC36 (V-J=2.34+/-0.18), which combined with previous measured colors in
the visible, indicate a red reflectivity spectrum at all wavelengths.
Photometric V-band lightcurves were taken for both objects over a time span of
around 8 hours. We have determined a possible rotational period of P=10.1+/-0.8
h for 1998 SN165, making it the seventh TNO with an estimated period. From its
lightcurve variation of Dm=0.151(+0.022/-0.030), we have inferred an asymmetry
ratio of a/b >=1.148(+0.024/-0.031). For 1999 TC36, we did not detect any
rotational period or periodic signal variation within the uncertainties, but
the analysis of its lightcurve hints to a slight systematic magnitude decrease.Comment: Accepted for publication in New Astronomy (13 pages, inc. 4 figures
Bringing Foundations and Governments Closer. A Cross-Country Analysis
This report is based on the findings of four case studies undertaken in India, Kenya, Mexicoand Myanmar between 2014 and 2016. Key partners in these countries who contributed to the case studies were:* India: Dasra* Kenya: Office of the Deputy President (ODP), SDG Philanthropy Platform (SDGPP), and theEast Africa Association of Grantmakers (EAAG)* Mexico: Mexican Agency for International Development Co-operation (AMEXCID), GIZ, theMexican Centre for Philanthropy (CEMEFI), Centro de Investigación y Estudios sobreSociedad Civil (CIESC) and Universidad Autónoma Metropolitana (UAM)* Myanmar: British Council and HamsaHu
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