123 research outputs found
Weyl structures with positive Ricci tensor
We prove the vanishing of the first Betti number on compact manifolds
admitting a Weyl structure whose Ricci tensor satisfies certain positivity
conditions, thus obtaining a Bochner-type vanishing theorem in Weyl geometry.
We also study compact Hermitian-Weyl manifolds with non-negative symmetric part
of the Ricci tensor of the canonical Weyl connection and show that every such
manifold has first Betti number and Hodge numbers for
, , for .Comment: 8 pages, Latex format, no figures; added section; to appear in Diff.
Geom. App
Linear perturbations of quaternionic metrics
We extend the twistor methods developed in our earlier work on linear
deformations of hyperkahler manifolds [arXiv:0806.4620] to the case of
quaternionic-Kahler manifolds. Via Swann's construction, deformations of a
4d-dimensional quaternionic-Kahler manifold are in one-to-one
correspondence with deformations of its -dimensional hyperkahler cone
. The latter can be encoded in variations of the complex symplectomorphisms
which relate different locally flat patches of the twistor space , with a
suitable homogeneity condition that ensures that the hyperkahler cone property
is preserved. Equivalently, we show that the deformations of can be encoded
in variations of the complex contact transformations which relate different
locally flat patches of the twistor space of , by-passing the Swann
bundle and its twistor space. We specialize these general results to the case
of quaternionic-Kahler metrics with commuting isometries, obtainable by
the Legendre transform method, and linear deformations thereof. We illustrate
our methods for the hypermultiplet moduli space in string theory
compactifications at tree- and one-loop level.Comment: 55 pages, 1 figure, uses JHEP3.cls; v2: one ref added, minor
improvements; v3: title changed, sections 2.5 and 5.2 rewritten in part, ref
[26] adde
Early Bronze Age Barrow Graves in North-West Bulgaria
Ten Early Bronze Age barrows with 20 mortuary complexes from North-West Bulgaria
are presented in this paper. The earliest barrow grave in North-West Bulgaria is argued to be Tarnak,
“Ninovska barrow”, grave No. 2 that could be dated to Cernavodă І – Cernavodă ІІІ period; the other
graves being chronologically assigned to EBA-1b (Zimnicea-Celei), EBA-2 and, EBA-3 periods.
Possible relations between “Yamnaya” and local populations in the region are discussed as well
Self-dual Einstein Spaces, Heavenly Metrics and Twistors
Four-dimensional quaternion-Kahler metrics, or equivalently self-dual
Einstein spaces M, are known to be encoded locally into one real function h
subject to Przanowski's Heavenly equation. We elucidate the relation between
this description and the usual twistor description for quaternion-Kahler
spaces. In particular, we show that the same space M can be described by
infinitely many different solutions h, associated to different complex (local)
submanifolds on the twistor space, and therefore to different (local)
integrable complex structures on M. We also study quaternion-Kahler
deformations of M and, in the special case where M has a Killing vector field,
show that the corresponding variations of h are related to eigenmodes of the
conformal Laplacian on M. We exemplify our findings on the four-sphere S^4, the
hyperbolic plane H^4 and on the "universal hypermultiplet", i.e. the
hypermultiplet moduli space in type IIA string compactified on a rigid
Calabi-Yau threefold.Comment: 44 pages, 1 figure; misprints correcte
Benchmarking in a rotating annulus: a comparative experimental and numerical study of baroclinic wave dynamics
The differentially heated rotating annulus is a widely studied tabletop-size
laboratory model of the general mid-latitude atmospheric circulation. The two
most relevant factors of cyclogenesis, namely rotation and meridional
temperature gradient are quite well captured in this simple arrangement. The
radial temperature difference in the cylindrical tank and its rotation rate can
be set so that the isothermal surfaces in the bulk tilt, leading to the
formation of baroclinic waves. The signatures of these waves at the free water
surface have been analyzed via infrared thermography in a wide range of
rotation rates (keeping the radial temperature difference constant) and under
different initial conditions. In parallel to the laboratory experiments, five
groups of the MetStr\"om collaboration have conducted numerical simulations in
the same parameter regime using different approaches and solvers, and applying
different initial conditions and perturbations. The experimentally and
numerically obtained baroclinic wave patterns have been evaluated and compared
in terms of their dominant wave modes, spatio-temporal variance properties and
drift rates. Thus certain ``benchmarks'' have been created that can later be
used as test cases for atmospheric numerical model validation
SU(3)-instantons and -heterotic string solitons
Necessary and sufficient conditions to the existence of a hermitian
connection with totally skew-symmetric torsion and holonomy contained in SU(3)
are given. Non-compact solution to the supergravity-type I equations of motion
with non-zero flux and non-constant dilaton is found in dimensions 6.
Non-conformally flat non-compact solutions to the supergravity-type I equations
of motion with non-zero flux and non-constant dilaton are found in dimensions 7
and 8. A Riemannian metric with holonomy contained in arises from our
considerations and Hitchin's flow equations, which seems to be new. Compact
examples of and instanton satisfying the anomaly
cancellation conditions are presented.Comment: LaTex, 22 pages, Corrected anomaly cancellation, final version to
appear in Commun. Math. Phy
Supergravity description of spacetime instantons
We present and discuss BPS instanton solutions that appear in type II string
theory compactifications on Calabi-Yau threefolds. From an effective action
point of view these arise as finite action solutions of the Euclidean equations
of motion in four-dimensional N=2 supergravity coupled to tensor multiplets. As
a solution generating technique we make use of the c-map, which produces
instanton solutions from either Euclidean black holes or from Taub-NUT like
geometries.Comment: 35 pages, some clarifications adde
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