Deformation theory of nearly K\"ahler manifolds

Nearly K\"ahler manifolds are the Riemannian 6-manifolds admitting real Killing spinors. Equivalently, the Riemannian cone over a nearly K\"ahler manifold has holonomy contained in G2. In this paper we study the deformation theory of nearly K\"ahler manifolds, showing that it is obstructed in general. More precisely, we show that the infinitesimal deformations of the homogeneous nearly K\"ahler structure on the flag manifold are all obstructed to second order

New G2 holonomy cones and exotic nearly Kaehler structures on the 6-sphere and the product of a pair of 3-spheres

There is a rich theory of so-called (strict) nearly Kaehler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kaehler 6-manifolds play a distinguished role both in the general structure theory and also because of their connection with singular spaces with holonomy group the compact exceptional Lie group G2: the metric cone over a Riemannian 6-manifold M has holonomy contained in G2 if and only if M is a nearly Kaehler 6-manifold. A central problem in the field has been the absence of any complete inhomogeneous examples. We prove the existence of the first complete inhomogeneous nearly Kaehler 6-manifolds by proving the existence of at least one cohomogeneity one nearly Kaehler structure on the 6-sphere and on the product of a pair of 3-spheres. We conjecture that these are the only simply connected (inhomogeneous) cohomogeneity one nearly Kaehler structures in six dimensions.Comment: v2: Minor correction to proof of inhomogeneity of new nearly Kaehler structure in Theorem 7.12. Added Remark 7.13 on further consequences of the revised argument. Added two further references. v3: Corrected several typos and minor imprecisions; made minor expositional improvements suggested by referee; streamlined Section 9. To appear in the Annals of Mathematic

A portfolio diversification strategy via tail dependence measures

We provide a two-stage portfolio selection procedure in order to increase the diversification benefits in a bear market. By exploiting tail dependence-based risky measures a first-step cluster analysis is carried out for discerning between assets with the same performance during risky scenarios. Then a mean-variance efficient frontier is computed by fixing a number of assets per portfolio and by selecting only one item from each cluster. Empirical calculations on the EURO STOXX 50 prove that investing on selected index components in trouble periods may improve the risk-averse investor portfolio performance

Effects of photoperiod on epididymal and sperm morphology in a wild rodent, the viscacha (Lagostomus maximus maximus)

The viscacha (Lagostomus maximus maximus) is a seasonal South American wild rodent. The adult males exhibit an annual reproductive cycle with periods of maximum and minimum gonadal activity. Four segments have been identified in the epididymis of this species: initial, caput, corpus, and cauda. The main objective of this work was to relate the seasonal morphological changes observed in the epididymal duct with the data from epididymal sperm during periods of activity and gonadal regression using light and scanning electron microscopy (SEM). Under light and electron microscopy, epididymal corpus and cauda showed marked seasonal variations in structural parameters and in the distribution of different cellular populations of epithelium. Initial and caput segments showed mild morphological variations between the two periods. Changes in epididymal sperm morphology were observed in the periods analyzed and an increased number of abnormal gametes were found during the regression period. During this period, anomalies were found mainly in the head, midpiece, and neck, while in the activity period, defects were found only in the head. Our results confirm that the morphological characteristics of the epididymal segments, as well as sperm morphology, undergo significant changes during the reproductive cycle of Lagostomus.Fil: Cruceño, A. M.. Universidad Nacional de San Luis. Facultad de Química, Bioquímica y Farmacia. Cátedra de Histología; ArgentinaFil: De Rosas, J. C.. Consejo Nacional de Investigaciones Científicas y Tecnicas. Centro Cientifico Tecnologico Mendoza. Instituto Histologia y Embriologia de Mendoza "Dr. M. Burgos"; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Médicas; ArgentinaFil: Foscolo, Mabel Rosa. Consejo Nacional de Investigaciones Científicas y Tecnicas. Centro Cientifico Tecnologico Mendoza. Instituto Histologia y Embriologia de Mendoza "Dr. M. Burgos"; ArgentinaFil: Chaves, E. M.. Universidad Nacional de San Luis. Facultad de Química, Bioquímica y Farmacia. Cátedra de Histología; ArgentinaFil: Scardapane, L.. Universidad Nacional de San Luis. Facultad de Química, Bioquímica y Farmacia. Cátedra de Histología; ArgentinaFil: Dominguez, S.. Universidad Nacional de San Luis. Facultad de Química, Bioquímica y Farmacia. Cátedra de Histología; ArgentinaFil: Aguilera Merlo, C.. Universidad Nacional de San Luis. Facultad de Química, Bioquímica y Farmacia. Cátedra de Histología; Argentin

ALF gravitational instantons and collapsing Ricci-flat metrics on the <b><i>K</i>3</b> surface

We construct large families of new collapsing hyperkähler metrics on the K3 surface. The limit space is a flat Riemannian 3-orbifold T3/Z2. Away from finitely many exceptional points the collapse occurs with bounded curvature. There are at most 24 exceptional points where the curvature concentrates, which always contains the 8 fixed points of the involution on T3. The geometry around these points is modelled by ALF gravitational instantons: of dihedral type (Dk) for the fixed points of the involution on T3 and of cyclic type (Ak) otherwise. The collapsing metrics are constructed by deforming approximately hyperkähler metrics obtained by gluing ALF gravitational instantons to a background (incomplete) S1–invariant hyperkähler metric arising from the Gibbons–Hawking ansatz over a punctured 3-torus. As an immediate application to submanifold geometry, we exhibit hyperkähler metrics on the K3 surface that admit a strictly stable minimal sphere which cannot be holomorphic with respect to any complex structure compatible with the metric

Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds

We present an analytic construction of complete non-compact 8-dimensional Ricci-flat manifolds with holonomy Spin(7). The construction relies on the study of the adiabatic limit of metrics with holonomy Spin(7) on principal Seifert circle bundles over asymptotically conical G2 orbifolds. The metrics we produce have an asymptotic geometry, so-called ALC geometry, that generalises to higher dimensions the geometry of 4-dimensional ALF hyperk\"ahler metrics. We apply our construction to asymptotically conical G2 metrics arising from self-dual Einstein 4-orbifolds with positive scalar curvature. As illustrative examples of the power of our construction, we produce complete non-compact Spin(7) manifolds with arbitrarily large second Betti number and infinitely many distinct families of ALC Spin(7) metrics on the same smooth 8-manifold