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 -vectors reveal geometric Lefschetz-like decompositions of flag spheres.
Estimates small eigenvalues for geometrically finite manifolds.
Tensor approach simplifies Euclidean space descriptions.
Boosting framework for vector-valued prediction with geometric stability.
Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a manifold with a triangulated boundary. These invariants can be naturally united in a …
Geometric vector perceptrons improve protein structure learning.
A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the geometric type and their auto-Backlund transformations are found.
In this paper, we examine some geometric vector fields on 2-step nilmanifolds of dimension 5.
Study geometric flows with varying parameters and prove continuous dependence.
Study essential spectrum of differential operators on geometrically finite orbifolds.
In this article, we give a geometric proof of the classification of complex vector cross product due to Lee-Leung.
Geometric structures on surfaces relate to 2-plane distributions in 5D.
Study foliations on Riemannian manifolds with specific vector fields, focusing on geometric properties.
Our aim in this paper is to investigate some geometrical properties of Berger Spheres i.e. homogeneous Ricci solitons and harmonicity properties of invariant vector fields. We determine all vector fields which are critical points for the energy functional restricted to vector fields. We also see that do not exist any v…
Geometric structures on -manifolds, i.e.~non-negatively graded manifolds with an homological vector field, encode non-graded geometric data on Lie algebroids and their higher analogues. A particularly relevant class of structures consists of vector bundle valued differential forms. Symplectic forms, contac…
In this paper, we study face vectors of simplicial posets that are the face posets of cell decompositions of topological manifolds without boundary. We characterize all possible face vectors of simplicial posets whose geometric realizations are homeomorphic to the product of spheres. As a corollary, we obtain the chara…
In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field ξare discribed and Ricci soliton in perfect fluid spacetime with torse-forming vector field ξare determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given.
The standard Laplace operator is a generalization of the Hodge Laplace operator on differential forms to arbitrary geometric vector bundles, alternatively it can be seen as generalization of the Casimir operator acting on sections of homogeneous vector bundles over symmetric spaces to general Riemannian manifolds. Stre…
We consider the oscillator group equipped with a bi-invariant Lorentzian metric, and then some geometrical properties of this group i.e. homogeneous Ricci solitons and harmonicity properties of invariant vector fields are obtained. We also determine all vector fields which are critical points for the energy functional …
This paper explores geometric and analytic aspects of Lojasiewicz inequalities on vector bundles.
New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics like the projectability of a vector field to a hamiltonian vector field, the comput…
Study of generalized vector bundles and their geometric tools.
The paper geometrizes N-manifolds using symmetric vector bundles.
Study vector fields on hyperbolic spaces to create Ricci-Bourguignon solitons.
Equivalence of second order differential operators in vector bundles studied.
In this paper we introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution of this flow, discuss its convergence and possible applications, and its relation to the …
Geometrically describes surfaces with parallel mean curvature in warped product spaces.
Geometric Invariant Theory applied to Kähler manifolds yields analytic models for vector bundles.
Geometrically deforms algebras to Lie algebroids, revealing new invariants.
Introduces VB-structures for geometric objects on manifolds.
Study on solitons in deformed Kenmotsu manifolds with specific vector fields.
We develop a theory of parametrized geometric cobordism by introducing smooth Thom stacks. This requires identifying and constructing a smooth representative of the Thom functor acting on vector bundles equipped with extra geometric data, leading to a geometric refinement of the the Pontrjagin-Thom construction in stac…
Geometric equation defines canonical metrics on vector bundle families.
Geometrically convex return risk measures on AM-algebras
MLDL preserves manifold geometry in vector transformations.
Geometric analysis of nonlinear dynamics applied to financial time series.
Rotation minimizing vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even the curvature vanishes. Nevertheless, many other geometric properties have not been studied. In the present paper, RM vector fields along a curve immersed …
The paper classifies geometric structures of δ-almost Yamabe solitons on paracontact metric manifolds.
This article provides a pedagogically oriented introduction to geometric (Clifford) calculus on pseudo-Riemannian manifolds. Unlike usual approaches to the topic, which rely on embedding the geometric algebra either within a tensor algebra or within a vector manifold framework, here we define geometric calculus directl…
In this work we introduce the category of multiplicative sections of an $\la$-groupoid. We prove that this category carries natural strict Lie 2-algebra structures, which are Morita invariant. As applications, we study the algebraic structure underlying multiplicative vector fields on a Lie groupoid and in particular v…
The paper explores algebraic and geometric structures on parallelizable manifolds.
Geometrically proves twisted Poincaré duality for orientable Poisson manifolds.
The Complex Axis theorem states that any endomorphism of a finite-dimensional complex vector space affords an eigen-vector (or "invariant axis"). A geometric proof of this geometric result was given by A. de Medeiros, transforming the endomorphism into a topological self-map with Lefschetz number not equal to zero. We …
These notes are based on a series of five lectures given at the 2009 Villa de Leyva Summer School on Geometric and Topological Methods for Quantum Field Theory. The purpose of the lectures was to give an introduction to differential-geometric methods in the study of holomorphic vector bundles on a compact connected Rie…
Geometrically interprets cup products and defines combinatorial Pin structures.
We show that the category of vector fields on a geometric stack has the structure of a Lie 2-algebra. This proves a conjecture of R.~Hepworth. The construction uses a Lie groupoid that presents the geometric stack. We show that the category of vector fields on the Lie groupoid is equivalent to the category of vector fi…
Geometric models for representations up to homotopy using simplicial vector bundles.
This paper solves a problem in 3D geometry by defining a canonical partition for certain manifolds.