A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new method for computing image curvature efficiently and accurately.
We show how to compute tensor derivatives and curvature tensors using affine connections. This allows for all computations to be obtained without using coordinate systems, in a way that parallels the computations appearing in classical Riemannian Geometry. In particular, we obtain Bianchi identities for the curvature t…
We simplify evaluation of Ollivier-Ricci curvature bounds in hypergraphs.
New method for curvature computation in sub-Riemannian geometry.
New rational curvature measures for 2-complexes.
Researchers decompose Forman-Ricci curvature for efficient computation in VR complexes.
Explicit computation of Kontsevich weights for symplectic Poisson structures.
In this paper, we systematically compute the Bianchi identities for the canonical connection on an almost Hermitian manifold. Moreover, we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection. As applications of the c…
Authors compute Weingarten map and curvatures for SL(n, R).
We compute the Ricci curvature of a curved noncommutative three torus. The computation is done both for conformal and non-conformal perturbations of the flat metric. To perturb the flat metric, the standard volume form on the noncommutative three torus is perturbed and the corresponding perturbed Laplacian is analyzed.…
Based on two classical notions of curvature for curves in general metric spaces, namely the Menger and Haantjes curvatures, we introduce new definitions of sectional, Ricci and scalar curvature for networks and their higher dimensional counterparts. These new types of curvature, that apply to weighted and unweighted, d…
Computed formulas for curvature operators and Poincaré polynomials of symmetric spaces.
Verified numerics prove existence of a curvature solution with known symmetries.
ISAAC Newton uses input-based curvature for efficient training.
New curvature measure defined for graphs, with bounds on diameter and spectral gap.
In this paper we prove that the only algebraic constant mean curvature (cmc) surfaces in R^3 of order less than four are the planes, the spheres and the cylinders. The method used heavily depends on the efficiency of algorithms to compute Groebner Bases and also on the memory capacity of the computer used to do the com…
We compute the series expansions for the normal curvatures of hyperspheres, the Finsler and Rund curvatures of circles in Funk geometry as the radii tend to infinity. These three curvatures are different at infinity in Funk geometry.
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which have intersections with the original curves and surfaces at the singular points. …
In Sol space there are three uniparametric groups of isometries. In this work we study constant mean curvature surfaces invariant by one of these groups. We analyze the geometric properties of these surfaces by means of their computer graphics. We construct explicit examples of minimal surfaces and we shall relate …
We compute renormalized curvature integrals on Poincaré-Einstein manifolds.
We compute the curvature of the determinant line bundle on a family of Dirac operators for a noncommutative two torus. Following Quillen's original construction for Riemann surfaces and using zeta regularized determinant of Laplacians, one can endow the determinant line bundle with a natural Hermitian metric. By using …
We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.
-non-degenerate spaces are spacetimes that can be characterized uniquely by their scalar curvature invariants. The ultimate goal of the current work is to construct a basis for the scalar polynomial curvature invariants in three dimensional Lorentzian spacetimes. In particular, we seek a minimal set of alg…
The curvature tensor and the scalar curvature are computed in the space of positive definite real matrices endowed by the Kubo-Mori inner product as a Riemannian metric.
Study geodesic curvature of logarithmic spirals on curved surfaces.
We compute curvatures of a three-manifold formed by a Weil-Petersson geodesic in Teichmuller space.
We consider the problem of the combinatorial computation of the first Chern class of a circle bundle. N.Mnev found such a formula in terms of canonical shellings. It represents certain invariant of a triangulation computed by analyzing cyclic word in 3-character alphabet associated to the bundle. This curvature is a ki…
Researchers compute curvatures of Stiefel manifolds with new metrics.
In the present article we compute the flag curvature of a special type of invariant Kropina metrics on homogeneous spaces.
Study calculates reach and curvature of a specific geometric variety.
We have performed an empirical comparison of two distinct notions of discrete Ricci curvature for graphs or networks, namely, the Forman-Ricci curvature and Ollivier-Ricci curvature. Importantly, these two discretizations of the Ricci curvature were developed based on different properties of the classical smooth notion…
Proposes a method to estimate discrete curvatures for image reconstruction.
ViViT efficiently computes curvature for deep networks without approximations.
When undergraduates ask me what geometric group theorists study, I describe a theorem due to Gromov which relates the groups with an intrinsic geometry like that of the hyperbolic plane to those in which certain computations can be efficiently carried out. In short, I describe the close but surprising connection betwee…
Computed distortion coefficients for the α-Grushin plane.
New scalar curvature defined from Ollivier-Ricci curvature for graphs.
New method approximates Gaussian curvature on discrete surfaces.
We show that any contact form whose Fefferman metric admits a nonzero parallel vector field is pseudo-Einstein of constant pseudohermitian scalar curvature. As an application we compute the curvature groups of the total space of the canonical circle bundle over a CR manifold.
We interpret the setting for a Radon transform as a submanifold of the space of generalized functions, and compute its extrinsic curvature: it is the Hessian composed with the Radon transform.
The main result of the paper is a computation of the Ricci curvature of $\DS/S^1$. Unlike earlier results on the subject, we do not use the Kähler structure symmetries to compute the Ricci curvature, but rather rely on classical finite-dimensional results of Nomizu et al on Riemannian geometry of homogeneous spaces.
Conditions for torsion-free connections with specific curvature maps are derived.
In this paper we study sectional curvature of invariant hyper-Hermitian metrics on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. We give the Levi-Civita connections and explicit formulas for computing sectional curvatures of these metrics and show that all these spaces have …
The study examines Eschenburg orbifolds with positive sectional curvature and their geometric/topological properties.
In this short note, we use classic computations for Kähler-Ricci flow to achieve scalar curvature bound for minimal manifold of general type.
We study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly restrict to Dirac structures. Depending on an auxiliary affine connection K, we int…
We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein-Hilbert type of actions known from supergravity. In particular, we carefull…
In this article, using the generalized Newton transformation, we define higher order mean curvatures of distributions of arbitrary codimension and we show that they agree with the ones from Brito and Naveira (Ann. Global Anal. Geom. 18, 371-383 (2000)). We also introduce higher order mean curvature vector fields and we…
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 geometrically realize these results to produce a hypersurface with prescribed sectional curv…