Using renormalization group methods, we calculate the derivative expansion of the effective Lagrangian for a covariantly constant gauge field in curved spacetime. Curvature affects the vacuum; in particular it could induce phase transitions between different vacua. We also consider the effect of quantum fluctuations of the metric, in the context of a renormalizable R theory. In this case the cr...

Magnetization switching at the interface between ferromagnetic and paramagnetic metals, controlled by current-induced torques, could be exploited in magnetic memory technologies. Compelling questions arise regarding the role played in the switching by the spin Hall effect in the paramagnet and by the spin-orbit torque originating from the broken inversion symmetry at the interface. Of particula...

In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized δ-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent results concerning the Casorati curvature for a slant submanifold in a quaterni...

We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature, which is understood as the limit of the Ricci curvature of finite-dimensional groups, is calculated. We show that for some of these groups the Ricci curvatu...

where ω̃ = ( √ −1/2)g̃ij̄dz ∧ dz and Σ̃ = ( √ −1/2)R̃ij̄dz ∧ dz are the Kähler form, the Ricci form of the metric g̃ respectively, while c1(M) denotes the first Chern class. Under the normalized initial condition (2), the first author [3] (see also Proposition 1.1 in [4]) showed that the solution g(x, t) = ∑ gij̄(x, t)dz dz to the normalized flow (1) exists for all time. Furthermore by the work of Mok ...

Let f : X −→ S be a smooth projective family and let (L, h) be a singular hermitian line bundle on X with semipositive curvature current. Let Ks := K(Xs, KXs +L | Xs, h | Xs)(s ∈ S) be the Bergman kernel of KXs +L | Xs with respect to h | Xs and let hB the singular hermitian metric on KX + L defined by hB |Xs := 1/Ks. We prove that hB has semipositive curvature. This is a generalization of the ...

INTRODUCTION Accurate corneal measurements are crucial in corneal refractive surgery (CRS) to ensure successful outcomes. Soft contact lens (SCL) wear may result in changes to corneal curvature and structure. United States Food and Drug Administration (FDA) pre-operative guidelines recommend that prior to CRS, SCL wearers cease SCL wear for "at least two weeks before examination and treatment" ...

When considering the statistical properties of a bundle of cosmic microwave background (CMB) photons propagating through space, the effect of ‘mixing geodesics’ appears with a distinct signature that depends on the geometry of space. In a Universe with negative curvature this effect is expected to produce elongated anisotropy spots on CMB maps. We used COBE-DMR data to look for such effect. Bas...

We examine the effect of curvature on fast magnetoacoustic waves in dense coronal loops situated in a potential coronal arcade. The wave equation governing the velocity perturbations has been solved numerically under the zero-β approximation and in the absence of gravity. Due to the curvature of the structure, leaky waves arise. The extent of the leakage depends upon the length, width and densi...

The hypocotyl hook of the lettuce (Lactuca sativa cv. Grand Rapids) seedling is stimulated to a high degree of curvature through a synergistic interaction of ethylene and gibberellic acid in the light. Presentation of various inorganic salts to the seedlings caused extensive alteration of the hormone-induced curvatures, with ammonium and sulfate being the most stimulatory of curvature, and pota...