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 complete hypersurfaces found in affine geometry.
Study on completeness in affine and statistical geometry.
The paper explores fully affine maximal curves and their properties.
The paper proves an inequality and describes a curve flow in centro-affine geometry.
Comparison theorems in centro-affine differential geometry
The paper matches features in images using centro-affine invariants and heat flow.
The study examines closed manifolds with ray nil-affine structures and their completeness.
New theorem extends Hadamard's to transversely affine geometry.
In this paper we study the general affine differential geometry of surfaces in affine space . For a regular elliptical surface we define a moving frame of minimal order and get the complete system of differential invariants. As an application we classify regular elliptical surfaces of constant curvatures up to aff…
Abstract mathematical formulas for statistical structures and curvatures.
Geodesic connectedness proved for statistical manifolds with divisible cubic forms.
BN refines local partition geometry in piecewise-affine networks during training.
Study compares geometric approaches for shape and deformation statistics.
The paper explores affine geometry of line congruences using singularity theory.
Unified description of aesthetic curves through self-affinities.
The classical Fundamental Theorem of Affine Geometry states that for , any bijection of -dimensional Euclidean space that maps lines to lines (as sets) is given by an affine map. We consider an analogous characterization of affine automorphisms for compact quotients, and establish it for tori: A bijection o…
Main ideas of the differential geometry on affine bundles are presented. Affine counterparts of Lie algebroid and Poisson structures are introduced and discussed. The developed concepts are applied in a frame-independent formulation of the time-dependent and the Newtonian mechanics.
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…
New maximal surfaces solve Bernstein problems.
New formula for instantaneous frequency in unbalanced systems.
New formalization of curved spaces using pointwise affine spaces.
Survey on affine Anosov representations and their implications.
Let (M,w,L) be a symplectic manifold endowed with a lagrangian foliation L. Liberman and Weinstein have shown that the leaves of L are endowed with an affine structure. In this paper we provide links between the theories of affine manifolds and symplectic geometry. Using the work of Donaldson who have shown the existen…
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…
Algorithm finds optimal affine transformation to minimize overall distortion.
New calculus for invariant differential operators in parabolic geometries.
A frame independent formulation of analytical mechanics in the Newtonian space-time is presented. The differential geometry of affine values i.e., the differential geometry in which affine bundles replace vector bundles and sections of one dimensional affine bundles replace functions on manifolds, is used. Lagrangian a…
We examine the local geometry of affine surfaces which are locally symmetric. There are 6 non-isomorphic local geometries. We realize these examples as Type A, Type B, and Type C geometries using a result of Opozda and classify the relevant geometries up to linear isomorphism. We examine the geodesic structures in this…
Almost Zoll affine surface found on cylinder.
New insights from centro-affine geometry solve a key geometric conjecture.
The paper studies a specific centro-affine invariant hypersurface flow in R^(n+1).
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…
Smooth manifolds have been always understood intuitively as spaces with an affine geometry on the infinitesimal scale. In Synthetic Differential Geometry this can be made precise by showing that a smooth manifold carries a natural structure of an infinitesimally affine space. This structure is comprised of two pieces o…
The paper shows that energy futures yield curves have an affine geometry.
The aim of this paper is to investigate the differential geometry of immersed surfaces in three-dimensional normed spaces from the viewpoint of affine differential geometry. We endow the surface with a useful Riemannian metric which is closely related to normal curvature, and from this we re-calculate the Minkowski Gau…
Bi-forms extend contrast functions to handle torsion in information geometry.
New method computes affine normal directions efficiently for sparse polynomials.
New aesthetic curves in equiaffine geometry include the quadratic and logarithmic spiral.
In [DM] it was asked whether all flat holomorphic Cartan geometries (G,H) on a complex torus are translation invariant. We answer this affimatively under the assumption that the complex Lie group G is affine. More precisely, we show that every holomorphic Cartan geometry of type (G,H), with G a complex affine Lie group…
The paper proves new inequalities for convex hypersurfaces using centro-affine geometry.
The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for --graded parabolic geometries and for almost Grassmannian structures, in particular.…
Affine deformations of convex cones on projective surfaces.
The paper studies complex affine structures near irregular singularities.
The paper studies extremal hypersurfaces in ellipsoids using centro-affine geometry.
We show that the natural S^1-bundle over a projective special Kaehler manifold carries the geometry of a proper affine hypersphere endowed with a Sasakian structure. The construction generalizes the geometry of the Hopf-fibration $\Sr^{2n+1} \longrightarrow \CP^n$ in the context of projective special Kaehler manifolds.…
We uncover the lowest order differential invariants of Lagrangian submanifolds under affine symplectic maps, and find out what happens when they are constant.
In this paper we study the general affine geometry of curves in affine space . For a regular plane curves we define two kinds of moving frames. The first is of minimal order in all moving frames.The second is the Frenet moving frame. We get the moving equations of these moving frames. And we prove that curvature a…
Natural analogs of Lie brackets on affine bundles are studied, based on natural examples from differential geometry and analytical mechanics. In particular, a close relation to Lie algebroids and, by a sort of duality, to affine analogs of Poisson structures is established as well as affine versions of the complete lif…