3,637 research outputs found
Spinorial Characterization of Surfaces into 3-dimensional homogeneous Manifolds
We give a spinorial characterization of isometrically immersed surfaces into
3-dimensional homogeneous manifolds with 4-dimensional isometry group in terms
of the existence of a particular spinor, called generalized Killing spinor.
This generalizes results by T. Friedrich for and B. Morel for \Ss^3
and \HH^3. The main argument is the interpretation of the energy-momentum
tensor of a genralized Killing spinor as the second fondamental form up to a
tensor depending on the structure of the ambient spaceComment: 35 page
The Hijazi inequality on manifolds with boundary
In this paper, we prove the Hijazi inequality on compact Riemannian spin
manifolds under two boundary conditions: the condition associated with a
chirality operator and the Riemannian version of the \MIT bag condition. We
then show that the limiting-case is characterized as being a half-sphere for
the first condition whereas the equality cannot be achieved for the second.Comment: 14 page
Pricing Spread Options using Matched Asymptotic Expansions
This document deals with approximating spread options prices using Matched
Asymptotic Expansions techniques on the correlation. More precisely, it deals with spreads options on assets that are highly correlated (ρ ∼ 1), which is most commonly observed in Oil Markets (Crude Oil vs. Gasoline for example). We will first start by applying this methodology to exchange options before generalizing our results to spread options. Then we are going to describe an alternative approach of pricing spread options by approximating the bivariate normal distribution. Finally, we will see how we can apply our methodology to the case where we have more than two assets
Prefabricated foldable lunar base modular systems for habitats, offices, and laboratories
The first habitat and work station on the lunar surface undoubtedly has to be prefabricated, self-erecting, and self-contained. The building structure should be folded and compacted to the minimum size and made of materials of minimum weight. It must also be designed to provide maximum possible habitable and usable space on the Moon. For this purpose the concept of multistory, foldable structures was further developed. The idea is to contain foldable structural units in a cylinder or in a capsule adapted for launching. Upon landing on the lunar surface, the cylinder of the first proposal in this paper will open in two hinge-connected halves while the capsule of the second proposal will expand horizontally and vertically in all directions. In both proposals, the foldable structural units will self-erect providing a multistory building with several room enclosures. The solar radiation protection is maintained through regolith-filled pneumatic structures as in the first proposal, or two regolith-filled expandable capsule shells as in the second one, which provide the shielding while being supported by the erected internal skeletal structure
Eigenvalue estimates for the Dirac-Schr\"odinger operators
We give new estimates for the eigenvalues of the hypersurface Dirac operator
in terms of the intrinsic energy-momentum tensor, the mean curvature and the
scalar curvature. We also discuss their limiting cases as well as the limiting
cases of the estimates obtained by X. Zhang and O. Hijazi in [13] and [10]. We
compare these limiting cases with those corresponding to the Friedrich and
Hijazi inequalities. We conclude by comparing these results to intrinsic
estimates for the Dirac-Schr\"odinger operator D_f = D - f/2.Comment: 22 pages, LaTeX, to appear in Journal of Geometry and Physic
A holographic principle for the existence of parallel spinor fields and an inequality of Shi-Tam type
Suppose that is the -dimensional boundary of a
connected compact Riemannian spin manifold with
non-negative scalar curvature, and that the (inward) mean curvature of
is positive. We show that the first eigenvalue of the Dirac operator
of the boundary corresponding to the conformal metric
is at least and equality
holds if and only if there exists a parallel spinor field on . As a
consequence, if admits an isometric and isospin immersion with
mean curvature as a hypersurface into another spin Riemannian manifold admitting a parallel spinor field, then \begin{equation} \label{HoloIneq}
\int_\Sigma H\,d\Sigma\le \int_\Sigma \frac{H^2_0}{H}\, d\Sigma \end{equation}
and equality holds if and only if both immersions have the same shape operator.
In this case, has to be also connected. In the special case where
, equality in (\ref{HoloIneq}) implies that is an Euclidean
domain and is congruent to the embedding of in as its
boundary. We also prove that Inequality (\ref{HoloIneq}) implies the Positive
Mass Theorem (PMT). Note that, using the PMT and the additional assumption that
is a strictly convex embedding into the Euclidean space, Shi and Tam
\cite{ST1} proved the integral inequality \begin{equation}\label{shi-tam-Ineq}
\int_\Sigma H\,d\Sigma\le \int_\Sigma H_0\, d\Sigma, \end{equation} which is
stronger than (\ref{HoloIneq}) .Comment: arXiv admin note: text overlap with arXiv:1502.0408
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