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 approach to symmetries in teleparallel geometries with non-trivial isotropy groups.
Presented spherical symmetric teleparallel geometry frames and field equations.
Recently, an extension of teleparallelism to a Weyl geometry which allows us to easily establish conformal invariance and "geometrize" electromagnetism has been presented. In this paper, I extend a result which concerns the existence of the Schwarzschild solution to a particular class of this extension. In addition, I …
Bi-forms extend contrast functions to handle torsion in information geometry.
As is well known, both Weyl and Weitzenböck spacetimes were initially used as attempts to geometrize the electromagnetic field. In this letter, we prove that this field can also be regarded as a geometrical quantity in an extended version of the Weitzenböck spacetime. The new geometry encompasses features of both Weyl …
We show that general relativity can be viewed as a higher gauge theory involving a categorical group, or 2-group, called the teleparallel 2-group. On any semi-Riemannian manifold M, we first construct a principal 2-bundle with the Poincare 2-group as its structure 2-group. Any flat metric-preserving connection on M giv…
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…
The main result of the paper is a new representation for the Weyl Lagrangian (massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e. an orthonormal tetrad of covector fields. We write down a simple Lagrangian - wedge product of axial torsion with a lightlike element of the coframe - and show tha…
The main result of the paper is a new representation for the Weyl Lagrangian (massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e. an orthonormal tetrad of covector fields. We write down a simple Lagrangian - wedge product of axial torsion with a lightlike element of the coframe - and show tha…
The main result of the paper is a new representation of the Weyl Lagrangian (massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e. an orthonormal tetrad of covector fields. We write down a simple Lagrangian - wedge product of axial torsion with a lightlike element of the coframe - and show that…
We consider an elliptic self-adjoint first order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of our operator is assumed to be trace-free. We study the spectral function which is the sum of squar…
Study surfaces with constant ratio of principal curvatures in Euclidean and isotropic geometries.
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwe…
We define hermitian geometry as the target space geometry of the two dimensional supersymmetric sigma model. This includes generalised Kähler geometry for , generalised hyperkähler geometry for , strong Kähler with torsion geometry for and strong hyperkähler with torsion geometry f…
Non-lorentzian geometry reviewed, including Lie algebras and Klein geometries.
Simpler method derived for path geometries on surfaces, characterizing projective path geometries.
New definition of Born geometry connects to known geometries.
We give an introduction to the theory of varieties of minimal rational tangents, emphasizing its aspect as a fusion of algebraic geometry and differential geometry, more specifically, a fusion of Mori geometry of minimal rational curves and Cartan geometry of cone structures.
The paper extends group constructions to coset geometries, creating new ways to combine geometries.
New symmetries found in Riemann-Cartan geometries.
Survey explores interactions between convex and complex geometry.
Lecture notes on geodesics in differential geometry.
Lecture notes on Finslerian geometry.
Spin(7) geometry linked to multisymplectic geometry.
The extension functors between categories of Cartan geometries can be used to define different categories of Cartan geometries with additional morphisms. The Cartan geometries modeled on skeletons can be used for the description of such categories of Cartan geometries and therefore we develop the theory of Cartan geome…
A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study transitions, one must define a notion of geometric limit at the level of homogeneous spac…
Paper introduces a generalized Bures-Wasserstein geometry for SPD matrices.
We show that a car, viewed as a nonholonomic system, provides an example of a flat parabolic geometry of type , where is a Borel parabolic subgroup in . We discuss the relations of this geometry of a car with the geometry of circles in the plane (a low dimensional Lie sph…
The study sets limits on the complexity of Klein geometries.
Surveying probabilistic real algebraic geometry.
Develops Weyl structures for path geometries, simplifying their study.
Ray-marching method visualizes 8 Thurston geometries in real-time.
The paper extends Ruh-Vilms theorem to hypersurfaces in Weitzenböck geometry.
Paper develops formulas and theorems in Hermitian geometry.
Introduces a new geometry based on difference angles, showing unique properties.
The study of special metrics in various parabolic geometries.
We introduce the notion of manifolds of amalgamation geometry and its generalization, split geometry. We show that the limit set of any surface group of split geometry is locally connected, by constructing a natural Cannon-Thurston map.
KT-geometry is the geometry of a Hermitian connection whose torsion is a 3-form. HKT-geometry is the geometry of a hyper-Hermitian connection whose torsion is a 3-form. We identify non-trivial conditions for a reduction theory for these types of geometry.
We classify the 5-dimensional homogeneous geometries in the sense of Thurston. The present paper (part 3 of 3) classifies those in which the linear isotropy representation is nontrivial but reducible. Most of the resulting geometries are products. Some interesting examples include a countably infinite family of inequiv…
New framework for noncommutative Carrollian geometry using Lie-Rinehart pairs.
Authors discuss complex and non-Archimedean geometry, proving a conjecture.
The target space geometry of abelian vector multiplets in theories in four and five space-time dimensions is called special geometry. It can be elegantly formulated in terms of Hessian geometry. In this review, we introduce Hessian geometry, focussing on aspects that are relevant for the special geometrie…
New geometry based on Siegel upper half-space with volume formula.
Quantum field theory connects Riemannian geometry to quantum fluctuations.
Develops a new algebraic framework for differential geometry of infinite dimensional spaces.
Study of Teichmüller space geometry using infinitesimal and global methods.
The study identifies two sources of invariants in 2--nondegenerate CR geometries.
We will survey some aspects of the smooth topology, algebraic geometry, symplectic geometry and contact geometry of anti-canonical pairs in complex dimension two.