145 research outputs found
Curvature dependent lower bounds for the first eigenvalue of the Dirac operator
Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we
derive inequalities that involve a real parameter and join the eigenvalues of
the Dirac operator with curvature terms. The discussion of these inequalities
yields vanishing theorems for the kernel of the Dirac operator and lower
bounds for the spectrum of if the curvature satisfies certain conditions.Comment: Latex2e, 14p
Lower bounds for the first eigenvalue of the Dirac operator on compact Riemannian manifolds
AbstractSome new, improved, curvature depending lower bounds for the first eigenvalue of the Dirac operator on compact Riemannian manifolds are proved. If certain curvature conditions are satisfied, then these lower bounds are also useful in cases where the scalar curvature has zeros or attains negative values. This implies stronger vanishing theorems for harmonic spinors
K\"ahlerian Twistor Spinors
On a K\"ahler spin manifold K\"ahlerian twistor spinors are a natural
analogue of twistor spinors on Riemannian spin manifolds. They are defined as
sections in the kernel of a first order differential operator adapted to the
K\"ahler structure, called K\"ahlerian twistor (Penrose) operator. We study
K\"ahlerian twistor spinors and give a complete description of compact K\"ahler
manifolds of constant scalar curvature admitting such spinors. As in the
Riemannian case, the existence of K\"ahlerian twistor spinors is related to the
lower bound of the spectrum of the Dirac operator.Comment: shorter version; to appear in Math.
Relative commutants of strongly self-absorbing C*-algebras
The relative commutant of a strongly self-absorbing
algebra is indistinguishable from its ultrapower . This
applies both to the case when is the hyperfinite II factor and to the
case when it is a strongly self-absorbing C*-algebra. In the latter case we
prove analogous results for and reduced powers
corresponding to other filters on . Examples of algebras with
approximately inner flip and approximately inner half-flip are provided,
showing the optimality of our results. We also prove that strongly
self-absorbing algebras are smoothly classifiable, unlike the algebras with
approximately inner half-flip.Comment: Some minor correction
A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself
We give an example of an exact, stably finite, simple. separable C*-algebra D
which is not isomorphic to its opposite algebra. Moreover, D has the following
additional properties. It is stably finite, approximately divisible, has real
rank zero and stable rank one, has a unique tracial state, and the order on
projections over D is determined by traces. It also absorbs the Jiang-Su
algebra Z, and in fact absorbs the 3^{\infty} UHF algebra. We can also
explicitly compute the K-theory of D, namely K_0 (D) = Z[1/3] with the standard
order, and K_1 (D) = 0, as well as the Cuntz semigroup of D.Comment: 16 pages; AMSLaTeX. The material on other possible K-groups for such
an algebra has been moved to a separate paper (1309.4142 [math.OA]
Some integrability conditions for almost K\"ahler manifolds
Among other results, a compact almost K\"ahler manifold is proved to be
K\"ahler if the Ricci tensor is semi-negative and its length coincides with
that of the star Ricci tensor or if the Ricci tensor is semi-positive and its
first order covariant derivatives are Hermitian. Moreover, it is shown that
there are no compact almost K\"ahler manifolds with harmonic Weyl tensor and
non-parallel semi-positive Ricci tensor. Stronger results are obtained in
dimension 4.Comment: Latex2e, 13 page
Killing spinors in supergravity with 4-fluxes
We study the spinorial Killing equation of supergravity involving a torsion
3-form \T as well as a flux 4-form \F. In dimension seven, we construct
explicit families of compact solutions out of 3-Sasakian geometries, nearly
parallel \G_2-geometries and on the homogeneous Aloff-Wallach space. The
constraint \F \cdot \Psi = 0 defines a non empty subfamily of solutions. We
investigate the constraint \T \cdot \Psi = 0, too, and show that it singles
out a very special choice of numerical parameters in the Killing equation,
which can also be justified geometrically
The Dirac operator on generalized Taub-NUT spaces
We find sufficient conditions for the absence of harmonic spinors on
spin manifolds constructed as cone bundles over a compact K\"ahler base. These
conditions are fulfilled for certain perturbations of the Euclidean metric, and
also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a
conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page
Heat kernel coefficients for chiral bag boundary conditions
We study the asymptotic expansion of the smeared L2-trace of fexp(-tP^2)
where P is an operator of Dirac type, f is an auxiliary smooth smearing
function which is used to localize the problem, and chiral bag boundary
conditions are imposed. Special case calculations, functorial methods and the
theory of zeta and eta invariants are used to obtain the boundary part of the
heat-kernel coefficients a1 and a2.Comment: Published in J. Phys. A38, 2259-2276 (2005). Record without file
already exists on the SLAC recor
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