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 $b_1 =1$ and Hodge numbers $h^{p,0} =0$ for $p>0$, $h^{0,1} =1$, $h^{0,q} =0$ for $q>1$.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 $M$ are in one-to-one correspondence with deformations of its $4d+4$-dimensional hyperkahler cone $S$. The latter can be encoded in variations of the complex symplectomorphisms which relate different locally flat patches of the twistor space $Z_S$, with a suitable homogeneity condition that ensures that the hyperkahler cone property is preserved. Equivalently, we show that the deformations of $M$ can be encoded in variations of the complex contact transformations which relate different locally flat patches of the twistor space $Z_M$ of $M$, by-passing the Swann bundle and its twistor space. We specialize these general results to the case of quaternionic-Kahler metrics with $d+1$ 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 G2,Spin(7)G_2, Spin(7)-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 $G_2$ arises from our considerations and Hitchin's flow equations, which seems to be new. Compact examples of $SU(3), G_2$ and $Spin(7)$ 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