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.
New metrics for SPD matrices explore affine invariance and symmetry principles.
Let (E, \varphi) be a flat Higgs bundle on a compact special affine manifold M equipped with an affine Gauduchon metric. We prove that (E, \varphi) is polystable if and only if it admits an affine Yang-Mills-Higgs metric.
Affine spheres can be realized with a specific Blaschke metric condition.
The paper develops methods to generate invariant quantities in Metric-Affine Geometry.
Study of convex hypersurfaces with specific curvature properties.
Researchers develop geodesics for a new metric on correlation matrices.
We introduce a new family of affine metrics on a locally strictly convex surface in affine 4-space. Then, we define the symmetric and antisymmetric equiaffine planes associated with each metric. We show that if is immersed in a locally strictly convex hyperquadric, then the symmetric and the antisymmetric plane…
Unified gravity and electromagnetism using algebroid structures.
Curve shortening in metric-affine plane shrinks convex curves to points.
The affine-additive group is hyperbolic with a non-vanishing 4-capacity.
We develop the method of anholonomic frames with associated nonlinear connection (in brief, N--connection) structure and show explicitly how geometries with local anisotropy (various type of Finsler--Lagrange--Cartan--Hamilton geometry) can be modeled in the metric--affine spaces. There are formulated the criteria when…
Study centro-affine invariants on ellipses using canonical Lorentz metric.
Classifies connections on Galilei manifolds, generalizing known results.
Study on projective and affine equivalence of sub-Riemannian metrics on manifolds.
Integral formulas for metric-affine spaces with specific distributions.
In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connecti…
We develop a theory of stable bundles and affine Hermitian-Einstein metrics for flat vector bundles over a special affine manifold (a manifold admitting an atlas whose gluing maps are all locally constant volume-preserving affine maps). Our paper presents a parallel to Donaldson-Uhlenbeck-Yau's proof of the existence o…
Kunneth formula derived for flat affine manifolds and applied to Hessian metrics.
New findings show Berwald Finsler spacetimes cannot be metrized.
The paper proves the existence and uniqueness of Calabi-Yau metrics on affine spherical varieties.
Researchers found invariant metric connections on Berger spheres that are Einstein with skew torsion.
The paper explores properties of affine Szabó manifolds and their metrics.
On an affine flat manifold with coordinates x^j and convex local potential function f, we call the affine Kahler metric f_{ij} dx^i dx^j semi-flat Calabi-Yau if it satisfies det f_{ij} = 1. Recently Gross-Wilson have constructed many such metrics on S^2 minus 24 singularities, as degenerate limits of Calabi-Yau metrics…
New metrics defined for full-rank correlation matrices, ensuring unique operations.
Study of manifolds with flat connections and diagonal metrics leading to vanishing Euler characteristic.
Sasaki-Einstein metrics linked to K-stability in affine varieties.
Monochromatic Finsler metrics are shown to be generalized Berwald metrics.
Study non-integrable distributions with various affine connections.
We study the real Monge-Ampère equation in two and three dimensions, both from the point of view of the SYZ conjecture, where solutions give rise to semi-flat Calabi-Yau's and in affine differential geometry, where solutions yield parabolic affine sphere hypersurfaces. We find explicit examples, connect the holomorphic…
By considering the projectivized spectrum of the Jacobi operator, we introduce the concept of projective Osserman manifold in both the affine and in the pseudo-Riemannian settings. If M is an affine projective Osserman manifold, then the modified Riemannian extension metric on the cotangent bundle is both spacelike and…
This is an account of some aspects of the geometry of Kähler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for Kähler affine metrics of Yau's Schwarz lemma for volume forms. By a theorem of Chen…
A common approach to metric-affine, local Poincaré, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and we study both, absolute and relative simultaneity postulates, giving rise to altern…
The anholonomic frame method is generalized for non--Riemannian gravity models defined by string corrections to the general relativity and metric-affine gravity (MAG) theories. Such spacetime configurations are modeled as metric-affine spaces provided with generic off-diagonal metrics (which can not be diagonalized by …
In (equi-)affine differential geometry, the most important algebraic invariants are the affine (Blaschke) metric h, the affine shape operator S and the difference tensor K. A hypersurface is said to admit a pointwise symmetry if at every point there exists a linear transformation preserving the affine metric, the affin…
Notes on flat pseudo-Riemannian manifolds, focusing on their characterization and properties.
This paper is a review of the twistor theory of irreducible G-structures and affine connections. Long ago, Berger presented a very restricted list of possible irreducibly acting holonomies of torsion-free affine connections. His list was complete in the part of metric connections, while the situation with holonomies of…
The aim of this paper is to give a local description of affine surfaces, whose induced Blaschke structure is projectively flat. We show that such affine surfaces with constant Gauss affine curvature and indefinite induced Blaschke metric are described by soliton equations.
New infinite arrangements found in higher dimensions.
Study solutions to affine quasi-Einstein equation on homogeneous surfaces.
Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that they are critical points of an affine area functional defined on the space of qu…
We developed a perturbation model for affine gravity theories.
Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 s…
The paper examines properties of self-affine Sierpiński sponges using metric invariants.
The paper studies singularities in discrete indefinite affine minimal surfaces.
As seen in the works of Calabi, Cheng-Yau and Loftin, affine sphere equations have a close relationship with Kaehler-Einstein metrics. The main purpose of this note is to show that an equation analogous to those of hyperbolic affine spheres arises naturally from Kaehler-Einstein metrics on Einstein toric surfaces. The …
Constructs hyperbolic affine spheres and Calabi-Yau metrics.
In this paper we deal with quadratic metric-affine gravity, which we briefly introduce, explain and give historical and physical reasons for using this particular theory of gravity. Further, we introduce a generalisation of well known spacetimes, namely pp-waves. A classical pp-wave is a 4-dimensional Lorentzian spacet…
We describe all affine maps from a Riemannian manifold to a metric space and all possible image spaces.