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.
The Cartan-Kähler theorem is extended to Lie algebroids.
The study finds static solutions in symplectic curvature flow in 4D.
This paper addresses the problem of existence of generalized Landsberg structures on surfaces using the Cartan-Kähler Theorem and a Path Geometry approach.
Proves convergence of normal forms for infinite-dimensional Lie pseudo-group actions.
We apply the Cartan-Kahler theorem for the k-Dirac operator studied in Clifford analysis and to the parabolic version of this operator. We show that for k = 2 the tableaux of the first prolongations of these two operators are involutive. This gives us a new characterization of the set of initial conditions for the 2-D…
The k-Dirac operator is a differential operator which is natural to geometric structure of a parabolic type. We will give a set of initial conditions for this operator. In the proof of the claim we will need to adapt some parts from the theory of exterior differential systems to the setting of weighted differential ope…
The study explores special Ricci-Hessian equations on Kähler manifolds and identifies three types of solutions.
In [17] A. Rapcsák obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential equations. In this paper we investigate the integrability of the Rapcsák system, consisting of the Rapcsák equations and the homogeneity condition, by using the Spence…
Using the Cartan-Kahler theory, and results on real algebraic structures, we prove two embedding theorems. First, the interior of a smooth, compact 3-manifold may be isometrically embedded into a G_2-manifold as an associative submanifold. Second, the interior of a smooth, compact 4-manifold K, whose double has a trivi…
This text is the extended version of a talk given at 6th Meeting of Integrable Systems and Quantum Filed Theory at Peyresq hold from June 10 2006 to June 17, 2006 at Peyresq, France. The goal of this lecture is to give a brief introduction to Cartan-Kähler's theory. As examples to the application of this theory, we cho…
We prove involutivity of Einstein, Einstein-Maxwell and other field equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kahler theory are derived.
Analyzes the generality of solitons for structures.
We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan-Kähler theorem. We consider a linear partial differential operator given by the two Helmholtz conditions expressed in terms of semi-basic 1-forms and study its…
An almost complex structure J on a 4-manifold X may be described in terms of a rank 2 vector bundle E. A splitting of J consists of a pair of line bundles spanning E. A hypersurface M in X satisfying a nondegeneracy condition inherits a CR-structure from J and a path geometry from the splitting. Using the Cartan-Kähler…
We provide precise formulations and proofs of two theorems from Darboux's lectures on orthogonal systems. These results provide local existence and uniqueness of solutions to certain types of first order PDE systems where each equation contains a single derivative for which it is solved: \[\frac{\partial u_i}{\partial …
The projective metrizability problem can be formulated as follows: under what conditions the geodesics of a given spray coincide with the geodesics of some Finsler space, as oriented curves. In Theorem 3.8 we reformulate the projective metrizability problem for a spray in terms of a first-order partial differential ope…
We study the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed eigencurves, i.e. the eigenvector fields of the Jacobian of the flux are given. We formulate this as a typically overdetermined system of equations for the eigenvalues-to-be. Equivalent formulations in te…
By analogy with associative and co-associative cases we introduce a class of three-dimensional non-orientable submanifolds, of almost manifolds, modelled on planes lying in a special orbit. An application of the Cartan-Kähler theory shows that some three-manifold can be presented in this w…
We exploit the Cartan-Kähler theory to prove the local existence of real analytic quaternionic contact structures for any prescribed values of the respective curvature functions and their covariant derivatives at a given point on a manifold. We show that, in a certain sense, the different real analytic quaternionic con…
This article uses Cartan-Kähler theory to construct local conservation laws from covariantly closed vector valued differential forms, objects that can be given, for example, by harmonic maps between two Riemannian manifolds. We apply the article's main result to construct conservation laws for covariant divergence free…
In the last chapter of his book "The Algebraic Theory of Modular Systems " published in 1916, F. S. Macaulay developped specific techniques for dealing with " unmixed polynomial ideals " by introducing what he called " inverse systems ". The purpose of this paper is to extend such a point of view to differential module…
This paper extends to dimension 4 the results in the article "Second Order Families of Special Lagrangian 3-folds" by Robert Bryant. We consider the problem of classifying the special Lagrangian 4-folds in C^4 whose fundamental cubic at each point has a nontrivial stabilizer in SO(4). Points on special Lagrangian 4-fol…
AI generates theorems and proofs for training theorem provers.
Global inverse function theorem proved easily using Riemannian geometry.
A new comparison theorem for geometric spaces.
Paper develops formulas and theorems in Hermitian geometry.
The paper proves three circles theorems and Liouville type theorems for subharmonic and holomorphic functions.
Revises a theorem by Thurston, finding a counter-example and a weaker version.
Proofs for Moon's theorem and its generalization.
Analyzes Saito vanishing theorem using methods.
Investigates proving geometric theorems over complex and real numbers using tilings.
Extends symplectic reduction and theorem to Lie algebroids.
Paper generalizes complex Brunn-Minkowski theory and proves new extension theorems.
Proves Thurston's bounded image theorem for Haken manifolds.
Method upgrades limit theorems to mixing limit theorems for dynamical systems.
Formulates Index III lemma and Rauch III theorem with applications.
In LM, we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems LM in two directions. First we establish a family rigidity theorem for the Dirac operator on loop space twisted by general positive energy loop gr…
The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.
INT benchmark tests theorem proving agents' ability to generalize to unseen theorems.
Proves two theorems on odd-dimensional manifolds with boundary.
Sharp convergence theorem for sphere submanifolds proved.
A homological selection theorem for C-spaces, as well as, a finite-dimensional homological selection theorem is established. We apply the finite-dimensional homological selection theorem to obtain fixed-point theorems for usco homologically UV^n set-valued maps.
Abstracts a theorem for non-smooth maps in infinite dimensions.
Atiyah-Singer theorem links math fields, predicts topological insights.
Paper generalizes a theorem for real analytic singularities.
The paper proves injectivity and vanishing theorems on compact Kahler manifolds.
Several proofs of Fáry--Milnor theorem are presented.
Reidemeister's theorem proved using smooth functions and transversality.