An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended ∗email address: [email protected] to complex manifolds. Examples include the quantum sphere, the complex quantum projective spaces and the two-sheeted space.

We prove that an irreducible 3-manifold whose fundamental group satisfies a certain group-theoretic property called RFRS is virtually fibered. As a corollary, we show that 3-dimensional reflection orbifolds and arithmetic hyperbolic orbifolds defined by a quadratic form virtually fiber. These include the Seifert Weber dodecahedral space and the Bianchi groups. Moreover, we show that a taut sutu...

Large igneous provinces (LIPs) form in both oceanic and continental settings by the emplacement and eruption of voluminous magmas ranging from basalt to rhyolite in composition. Continental flood basalt provinces are the best studied LIPs and consist of crustal intrusive systems, extensive flood lavas and ignimbrites, and mafic volcaniclastic deposits in varying proportions. Intrusive rocks are...

The formation of amyloid fibers and their deposition in the body is a characteristic of a number of devastating human diseases. Here, we propose a structural model, based on X-ray diffraction data, for the basic structure of an amyloid fibril formed by using the variants of the B1 domain of IgG binding protein G of Streptococcus. The model for the fibril incorporates four beta sheets in a bundl...

We find identities between theta constants with rational characteristics evaluated at period matrix of R, a cyclic 3 sheeted cover of the sphere with 3k branch points λ1...λ3k. These identities follow from Thomae formula [BR]. This formula expresses powers of theta constants as polynomials in λ1...λ3k. We apply the representation of the symmetric group to find relations between the polynomials ...

It is shown that a two-brane world made of two domain walls can be seen as a noncommutative two-sheeted spacetime under certain assumptions. This equivalence implies a model-independent phenomenology: Matter swapping between the two 3-branes (or sheets) is predicted through fermionic oscillations induced by magnetic vector potentials. This phenomenon, which might be experimentally studied, coul...

We classify all functions satisfying non-trivial families of PVIα equations. It turns out that all of these 23 solutions are of geometric origin: they are related to deformations of elliptic surfaces as proved earlier by Doran. Similarly, we prove that the same solutions can be obtained from deformations of three-sheeted covers of P1 with branching locus consisting of four points. e-mail: basse...

A-patches[BCX94a] are implicit surfaces in Bernstein-Bezier(BB) form that are smooth and single-sheeted. In this paper, we present algorithms to utilize the extra degrees of freedom of these patches for local shape co·ntrol. A ray shooting scheme is also given to rapidly generate polygonal approximations of A-patches for graphic display. A distributed implementation of this scheme gives near "r...