We give a hyperkk ahler analogue of the classiication of compact homogeneous KK ahler manifolds. Namely we show that, for a compact semisimple Lie group G, the complete G-invariant hyperkk ahler manifolds which are also locally G c-homogeneous with respect to one of the complex structures are precisely the hy-perkk ahler metrics of Kronheimer, Biquard and Kovalev on coadjoint semisimple orbits ...

We present an analytic construction of complete non-compact 8-dimensional Ricci-flat manifolds with holonomy Spin(7). The relies on the study adiabatic limit metrics Spin(7) principal Seifert circle bundles over asymptotically conical G2 orbifolds. we produce have asymptotic geometry, so-called ALC that generalises to higher dimensions geometry 4-dimensional ALF hyperk\"ahler metrics. apply our...

A classical result of Bondal-Orlov states that a standard flip in birational geometry gives rise to fully faithful functor between derived categories coherent sheaves. We complete their embedding into semiorthogonal decomposition by describing the complement. As an application, we can lift "quadratic Fano correspondence" (due Galkin-Shinder) Grothendieck ring varieties smooth cubic hypersurface...

A broad overview of the current status of proton stability in unified models of particle interactions is given which includes non supersymmetric unification, SUSY and SUGRA unified models, unification based on extra dimensions, and string-M-theory models. The extra dimensional unification includes 5D and 6D and universal extra dimensional (UED) models, and models based on warped geometry. Proto...

We classify those manifolds mentioned in the title which have nite topological type. Namely we show that any such connected M 4n is isomorphic to a hyperkk ahler quotient of a at quaternionic vector space H d by an abelian group. We also show that a compact connected and simply connected 3-Sasakian manifold of dimension 4n ? 1 whose isometry group has rank n + 1 is isometric to a 3-Sasakian quo...

We study the hyperkk ahler metrics associated to minimal singularities in the nilpotent variety of a semisimple Lie group. We show that Kronheimer's 4-dimensional ALE spaces are naturally realized within the context of coadjoint orbits and can be thought of as certain moduli spaces of SU(2) invariant instantons on R 4 nf0g with appropriate boundary conditions. We also show that the hyperkk ahle...

Chronic eczematous hand dermatoses with and without contact allergies are complex diseases, which makes it a challenge to select the best treatment and obtain an optimal patient experience and a satisfactory treatment result. The aim of this study was to evaluate retrospectively the clinical effect and patient experience of local treatment with psoralen plus ultraviolet A (PUVA) soaks and TL01 ...