The 22-year cycle in the geomagnetic 27-day recurrences reflecting on the F2-layer ionization

Solar cycle variations of the amplitudes of the 27-day solar rotation period reflected in the geomagnetic activity index <i>A<sub>p</sub></i>, solar radio flux F10.7cm and critical frequency <i>fo</i>F2 for mid-latitude ionosonde station Moscow from the maximum of sunspot cycle 18 to the maximum of cycle 23 are examined. The analysis shows that there are distinct enhancements of the 27-day amplitudes for <i>fo</i>F2 and <i>A<sub>p</sub></i> in the late declining phase of each solar cycle while the amplitudes for F10.7cm decrease gradually, and the <i> fo</i>F2 and <i>A<sub>p</sub></i> amplitude peaks are much larger for even-numbered solar cycles than for the odd ones. Additionally, we found the same even-high and odd-low pattern of <i>fo</i>F2 for other mid-latitude ionosonde stations in Northern and Southern Hemispheres. This property suggests that there exists a 22-year cycle in the F2-layer variability coupled with the 22-year cycle in the 27-day recurrence of geomagnetic activity.<br><br> <b>Key words.</b> Ionosphere (mid-latitude ionosphere; ionosphere- magnetosphere interactions) – Magnetospheric physics (solar wind-magnetosphere interactions

Planetary and gravity wave signatures in the F-region ionosphere with impacton radio propagation predictionsand variability

The aim of this work within the WP 3.1 of the COST 271 Action is the characterization of the variability introduced in the F-region ionosphere by -Planetary Wave Signatures- (PWS) and -Gravity Wave Signatures- (GWS). Typical patterns of percentage of time occurrence and time duration of PWS, their climatology and main drivers, as well as their vertical and longitudinal structure have been obtained. Despite the above characterization, the spectral distribution of event duration is too broad to allow for a reasonable prediction of PWS from ionospheric measurements themselves. GWS with a regular morning/evening wave bursts and specific GWS events whose arising can be predicted have been evaluated. As above, their typical pattern of occurrence and time duration, and their vertical structure have been obtained. The latter events remain in the ionospheric variability during disturbed days while additional wave enhancements of auroral origin occur. However, both types of disturbances can be distinguished

Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as introduced and studied in previous papers in the series) but this paper is largely independent of that theory. We obtain a characterization, on a large family of projective bundles, of those `admissible' Kaehler classes (i.e., the ones compatible with the bundle structure in a way we make precise) which contain an extremal Kaehler metric. In many cases, such as on geometrically ruled surfaces, every Kaehler class is admissible. In particular, our results complete the classification of extremal Kaehler metrics on geometrically ruled surfaces, answering several long-standing questions. We also find that our characterization agrees with a notion of K-stability for admissible Kaehler classes. Our examples and nonexistence results therefore provide a fertile testing ground for the rapidly developing theory of stability for projective varieties, and we discuss some of the ramifications. In particular we obtain examples of projective varieties which are destabilized by a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely self-contained; partially replaces and extends math.DG/050151

A splitting theorem for Kahler manifolds whose Ricci tensors have constant eigenvalues

It is proved that a compact Kahler manifold whose Ricci tensor has two distinct, constant, non-negative eigenvalues is locally the product of two Kahler-Einstein manifolds. A stronger result is established for the case of Kahler surfaces. Irreducible Kahler manifolds with two distinct, constant eigenvalues of the Ricci tensor are shown to exist in various situations: there are homogeneous examples of any complex dimension n > 1, if one eigenvalue is negative and the other positive or zero, and of any complex dimension n > 2, if the both eigenvalues are negative; there are non-homogeneous examples of complex dimension 2, if one of the eigenvalues is zero. The problem of existence of Kahler metrics whose Ricci tensor has two distinct, constant eigenvalues is related to the celebrated (still open) Goldberg conjecture. Consequently, the irreducible homogeneous examples with negative eigenvalues give rise to complete, Einstein, strictly almost Kahler metrics of any even real dimension greater than 4.Comment: 18 pages; final version; accepted for publication in International Journal of Mathematic

Covariant derivative of the curvature tensor of pseudo-K\"ahlerian manifolds

It is well known that the curvature tensor of a pseudo-Riemannian manifold can be decomposed with respect to the pseudo-orthogonal group into the sum of the Weyl conformal curvature tensor, the traceless part of the Ricci tensor and of the scalar curvature. A similar decomposition with respect to the pseudo-unitary group exists on a pseudo-K\"ahlerian manifold; instead of the Weyl tensor one obtains the Bochner tensor. In the present paper, the known decomposition with respect to the pseudo-orthogonal group of the covariant derivative of the curvature tensor of a pseudo-Riemannian manifold is refined. A decomposition with respect to the pseudo-unitary group of the covariant derivative of the curvature tensor for pseudo-K\"ahlerian manifolds is obtained. This defines natural classes of spaces generalizing locally symmetric spaces and Einstein spaces. It is shown that the values of the covariant derivative of the curvature tensor for a non-locally symmetric pseudo-Riemannian manifold with an irreducible connected holonomy group different from the pseudo-orthogonal and pseudo-unitary groups belong to an irreducible module of the holonomy group.Comment: the final version accepted to Annals of Global Analysis and Geometr

Toric G_2 and Spin(7) holonomy spaces from gravitational instantons and other examples

Non-compact G_2 holonomy metrics that arise from a T^2 bundle over a hyper-Kahler space are discussed. These are one parameter deformations of the metrics studied by Gibbons, Lu, Pope and Stelle in hep-th/0108191. Seven-dimensional spaces with G_2 holonomy fibered over the Taub-Nut and the Eguchi-Hanson gravitational instantons are found, together with other examples. By considering the Apostolov-Salamon theorem math.DG/0303197, we construct a new example that, still being a T^2 bundle over hyper-Kahler, represents a non trivial two parameter deformation of the metrics studied in hep-th/0108191. We then review the Spin(7) metrics arising from a T^3 bundle over a hyper-Kahler and we find two parameter deformation of such spaces as well. We show that if the hyper-Kahler base satisfies certain properties, a non trivial three parameter deformations is also possible. The relation between these spaces with the half-flat structures and almost G_2 holonomy spaces is briefly discussed.Comment: 27 pages. Typos corrected. Accepted for publication in Commun.Math.Phy