Related papers: Scalar Curvature for the Noncommutative Two Torus

We present a noncommutative extension of Quantum Cosmology and study the Kantowski-Sachs (KS) cosmological model requiring that the two scale factors of the KS metric, the coordinates of the system, and their conjugate canonical momenta do…

In this work, we describe the geometric and probabilistic properties of a noncommutative 2- torus in a magnetic field. We study the volume invariance, integrated scalar curvature and volume form by using the method of perturbation by inner…

We algebraically compute all possible sectional curvature values for canonical algebraic curvature tensors, and use this result to give a method for constructing general sectional curvature bounds. We use a well-known method to…

In the initial conditions of the $3 + 1$ formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point.…

Let R be an algebraic curvature tensor for a non-degenerate inner product of signature(p,q) where q>4. If $\pi$ is a spacelike 2 plane, let $R(\pi)$ be the associated skew-symmetric curvature operator. We classify the algebraic curvature…

Starting from the Schwinger--Dyson equation and the renormalization group equation for the massless Wess--Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by…

A warped product with a spherical factor and a logarithmically concave warping function satisfies a scalar curvature rigidity of the Llarull type. We develop a scalar curvature rigidity of the Llarull type for a general class of domains in…

Drawing on analogies with the commutative case, the Wilsonian picture of renormalization is developed for noncommutative scalar field theory. The dimensionful noncommutativity parameter, theta, induces several new features. Fixed-points are…

We show that tilting modules for quantum groups over local Noetherian domains exist and that the indecomposable tilting modules are parametrized by their highest weight. For this we introduce a model category ${\mathcal X}={\mathcal…

We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix geometries. The approximation is carried out for both irrational and rational deformation parameters by embedding…

We give a complete proof of the result stated in an earlier article, that the general Einstein metric with a symmetry, an anti-self-dual Weyl tensor and nonzero scalar curvature is determined by a solution of the $SU(\infty)$-Toda field…

We give an explicit formula for the second variation of the logarithm of the Selberg zeta function, $Z(s)$, on Teichm\"uller space. We then use this formula to determine the asymptotic behavior as $\text{Re} (s) \to \infty$ of the second…

We classify spin structures on the noncommutative torus, and find that the noncommutative n-torus has 2^n spin structures, corresponding to isospectral deformations of spin structures on the commutative n-torus. For n>3 the classification…

We show how non-commutativity arises from commutativity in the double sigma model. We demonstrate that this model is intrinsically non-commutative by calculating the propagators. In the simplest phase configuration, there are two dual…

A theta surface in affine 3-space is the zero set of a Riemann theta function in genus 3. This includes surfaces arising from special plane quartics that are singular or reducible. Lie and Poincar\'e showed that theta surfaces are precisely…

The mobility of a Kaehler metric is the dimension of the space of metrics with which it is c-projectively equivalent. The mobility is at least two if and only if the Kaehler metric admits a nontrivial hamiltonian 2-form. After summarizing…

We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation…

Given a group $G$ with bounded torsion that acts properly on a systolic complex, we show that every solvable subgroup of $G$ is finitely generated and virtually abelian of rank at most $2$. In particular this gives a new proof of the above…

We continue the study of the question of when a pseudo-Riemannain manifold can be locally characterised by its scalar polynomial curvature invariants (constructed from the Riemann tensor and its covariant derivatives). We make further use…

A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played…