1,687 research outputs found
Parallel Mean Curvature Surfaces in Symmetric Spaces
We present a reduction of codimension theorem for surfaces with parallel mean
curvature in symmetric spaces
Surgery and the Spectrum of the Dirac Operator
We show that for generic Riemannian metrics on a simply-connected closed spin
manifold of dimension at least 5 the dimension of the space of harmonic spinors
is no larger than it must be by the index theorem. The same result holds for
periodic fundamental groups of odd order.
The proof is based on a surgery theorem for the Dirac spectrum which says
that if one performs surgery of codimension at least 3 on a closed Riemannian
spin manifold, then the Dirac spectrum changes arbitrarily little provided the
metric on the manifold after surgery is chosen properly.Comment: 23 pages, 4 figures, to appear in J. Reine Angew. Mat
Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems
We develop area and volume comparison theorems for the evolution of
spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds,
where one has a lower bound on the Ricci tensor along timelike curves, and an
upper bound on the mean curvature of the hypersurface. Using these results, we
give a new proof of Hawking's singularity theorem.Comment: 15 pages, LaTe
Metrics with Prescribed Ricci Curvature near the Boundary of a Manifold
Suppose is a manifold with boundary. Choose a point . We
investigate the prescribed Ricci curvature equation \Ric(G)=T in a
neighborhood of under natural boundary conditions. The unknown here is
a Riemannian metric. The letter in the right-hand side denotes a
(0,2)-tensor. Our main theorems address the questions of the existence and the
uniqueness of solutions. We explain, among other things, how these theorems may
be used to study rotationally symmetric metrics near the boundary of a solid
torus . The paper concludes with a brief discussion of the Einstein
equation on .Comment: 13 page
Randomizing world trade. II. A weighted network analysis
Based on the misleading expectation that weighted network properties always
offer a more complete description than purely topological ones, current
economic models of the International Trade Network (ITN) generally aim at
explaining local weighted properties, not local binary ones. Here we complement
our analysis of the binary projections of the ITN by considering its weighted
representations. We show that, unlike the binary case, all possible weighted
representations of the ITN (directed/undirected, aggregated/disaggregated)
cannot be traced back to local country-specific properties, which are therefore
of limited informativeness. Our two papers show that traditional macroeconomic
approaches systematically fail to capture the key properties of the ITN. In the
binary case, they do not focus on the degree sequence and hence cannot
characterize or replicate higher-order properties. In the weighted case, they
generally focus on the strength sequence, but the knowledge of the latter is
not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243
[physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011
Instantons and Killing spinors
We investigate instantons on manifolds with Killing spinors and their cones.
Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds,
nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and
3-Sasakian manifolds. We construct a connection on the tangent bundle over
these manifolds which solves the instanton equation, and also show that the
instanton equation implies the Yang-Mills equation, despite the presence of
torsion. We then construct instantons on the cones over these manifolds, and
lift them to solutions of heterotic supergravity. Amongst our solutions are new
instantons on even-dimensional Euclidean spaces, as well as the well-known
BPST, quaternionic and octonionic instantons.Comment: 40 pages, 2 figures v2: author email addresses and affiliations adde
Measurement of the branching ratios of the Z0 into heavy quarks
We measure the hadronic branching ratios of the Z0 boson into heavy quarks:
Rb=Gamma(Z0->bb)/Gamma(Z0->hadrons) and Rc=Gamma(Z0->cc/Gamma(Z0->hadrons)
using a multi-tag technique. The measurement was performed using about 400,000
hadronic Z0 events recorded in the SLD experiment at SLAC between 1996 and
1998. The small and stable SLC beam spot and the CCD-based vertex detector were
used to reconstruct bottom and charm hadron decay vertices with high efficiency
and purity, which enables us to measure most efficiencies from data. We obtain,
Rb=0.21604 +- 0.00098(stat.) +- 0.00073(syst.) -+ 0.00012(Rc) and, Rc= 0.1744
+- 0.0031(stat.) +- 0.0020(syst.) -+ 0.0006(Rb)Comment: 37 pages, 8 figures, to be submitted to Phys. Rev. D version 2:
changed title to ratios, used common D production fractions for Rb and Rc and
corrected Zgamma interference. Identical to PRD submissio
Direct Measurements of A_b and A_c using Vertex/Kaon Charge Tags at SLD
Exploiting the manipulation of the SLC electron-beam polarization, we present
precise direct measurements of the parity violation parameters A_c and A_b in
the Z boson - c quark and Z boson - b quark coupling. Quark/antiquark
discrimination is accomplished via a unique algorithm that takes advantage of
the precise SLD CCD vertex detector, employing the net charge of displaced
vertices as well as the charge of kaons that emanate from those vertices. From
the 1996-98 sample of 400,000 Z decays, produced with an average beam
polarization of 73.4%, we find A_c = 0.673 +/- 0.029 (stat.) +/- 0.023 (syst.)
and A_b = 0.919 +/- 0.018 (stat.) +/- 0.017 (syst.).Comment: 11 pages, 2 figures, 2 tables, to be submitted to Physical Review
Letters; version 2 reflects changes suggested by the refere
Search for time-dependent B0s - B0s-bar oscillations using a vertex charge dipole technique
We report a search for B0s - B0s-bar oscillations using a sample of 400,000
hadronic Z0 decays collected by the SLD experiment. The analysis takes
advantage of the electron beam polarization as well as information from the
hemisphere opposite that of the reconstructed B decay to tag the B production
flavor. The excellent resolution provided by the pixel CCD vertex detector is
exploited to cleanly reconstruct both B and cascade D decay vertices, and tag
the B decay flavor from the charge difference between them. We exclude the
following values of the B0s - B0s-bar oscillation frequency: Delta m_s < 4.9
ps-1 and 7.9 < Delta m_s < 10.3 ps-1 at the 95% confidence level.Comment: 18 pages, 3 figures, replaced by version accepted for publication in
Phys.Rev.D; results differ slightly from first versio
Causal structures and causal boundaries
We give an up-to-date perspective with a general overview of the theory of
causal properties, the derived causal structures, their classification and
applications, and the definition and construction of causal boundaries and of
causal symmetries, mostly for Lorentzian manifolds but also in more abstract
settings.Comment: Final version. To appear in Classical and Quantum Gravit
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