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.
This article connects PCS structures to parabolic contact structures.
The paper explores symplectic fillability of specific contact structures on torus bundles.
We generalize the concept of locally symmetric spaces to parabolic contact structures. We show that symmetric normal parabolic contact structures are torsion--free and some types of them have to be locally flat. We prove that each symmetry given at a point with non--zero harmonic curvature is involutive. Finally we giv…
The chains studied in this paper generalize Chern-Moser chains for CR structures. They form a distinguished family of one dimensional submanifolds in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure and the system of chains can be equivalently encoded as Cartan geometries (of d…
Lie contact structures generalize the classical Lie sphere geometry of oriented hyperspheres in the standard sphere. They can be equivalently described as parabolic geometries corresponding to the contact grading of orthogonal real Lie algebra. It follows the underlying geometric structure can be interpreted in several…
Solved the equivalence problem for quaternionic contact structures.
Spinors help study unique five-dimensional contact structures.
Normalizes pseudo-Einstein contact forms for easier analysis.
Study new -contact distributions and Lie systems.
First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth systems of involutive symmetries can be obtained this way. Further, we investigate …
Study contact structures on flag varieties, proving a conjecture.
The moving coframe method is applied to solve the local equivalence problem for the class of linear parabolic equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and the complete sets of differential invariants for symmetry groups are found. The…
Study of differential operators in PCS structures using contactifications.
Study on parabolic points and cylindrical surfaces in Euclidean 3-space.
2-jets determine symmetries of parabolic geometries.
Unified PDE models from Lie algebras.
We find normal forms for parabolic Monge-Ampere equations. Of these, the most general one holds for any equation admitting a complete integral. Moreover, we explicitly give the determining equation for such integrals; restricted to the analytic case, this equation is shown to have solutions. The other normal forms exha…
Quantizes contact structures using dynamical methods.
The notion of special symplectic connections is closely related to contact parabolic geometries due to the work of M. Cahen and L. Schwachhöfer. We remind their characterization and reinterpret the result in terms of generalized Weyl connections. The aim of this paper is to provide an alternative and more explicit cons…
Contact projective structures have been profoundly studied by D.J.F. Fox. He associated to a contact projective structure a canonical projective structure on the same manifold. We interpret Fox' construction in terms of the equivalent parabolic (Cartan) geometries, showing that it is an analog of Fefferman's constructi…
The paper explores automorphism groups of parabolic structures on aspherical manifolds.
A flying saucer's flight is mathematically modeled with geometric structures.
According to a theorem of Eliashberg and Thurston a -foliation on a closed 3-manifold can be -approximated by contact structures unless all leaves of the foliation are spheres. Examples on the 3-torus show that every neighbourhood of a foliation can contain non-diffeomorphic contact structures. In this paper …
Study variational properties of cone structures with infinitesimal symmetry.
Using the theory of Weyl structures, we give a natural generalization of the notion of essential conformal structures and conformal Killing fields to arbitrary parabolic geometries. We show that a parabolic structure is inessential whenever the automorphism group acts properly on the base space. As a corollary of the g…
We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit description. This allows us to describe the structure of symmetric geometric structur…
Study aerodynamics of flying saucers on curved spaces.
New -geometries linked in 5D and 7D.
We apply the theory of Weyl structures for parabolic geometries developed by A. Cap and J. Slovak in to compute, for a quaternionic contact (qc) structure, the Weyl connection associated to a choice of scale, i.e. to a choice of Carnot-Carathéodory metric in the conformal class. The result of this computation has appli…
We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de-Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For regular normal geometries, this description can be related to the underlying geome…
We study vector fields generating a local flow by automorphisms of a parabolic geometry with higher order fixed points. We develop general tools extending the techniques of [1], [2], and [3]. We apply these tools to almost Grassmannian, almost quaternionic, and contact parabolic geometries, including CR structures, to …
On contact manifolds we describe a notion of (contact) finite-type for linear partial differential operators satisfying a natural condition on their leading terms. A large class of linear differential operators are of finite-type in this sense, and for any such operator we construct a partial connection on a (finite ra…
We consider Legendrian contact structures on odd-dimensional complex analytic manifolds. We are particularly interested in integrable structures, which can be encoded by compatible complete systems of second order PDEs on a scalar function of many independent variables and considered up to point transformations. Using …
The study of special metrics in various parabolic geometries.
In this note, we prove that the CR manifold which is induced from the canonical parabolic geometry of a quaternionic contact (qc) manifold via a Fefferman-type construction is equivalent to the CR twistor space of the qc manifold defined by O. Biquard.
BGG-sequences offer a uniform construction for invariant differential operators for a large class of geometric structures called parabolic geometries. For locally flat geometries, the resulting sequences are complexes, but in general the compositions of the operators in such a sequence are nonzero. In this paper, we sh…
Study CR manifolds focusing on Levi and contact-nondegeneracy.
Investigate the local geometry of smooth surfaces in 4-space via contact with 2-planes and apparent contours.
Abstract: Study of surface transitions and IDE inflections via contact geometry.
A car's motion shows flat parabolic geometry.
This paper analyses the parabolic geometries generated by a free 3-distribution in the tangent space of a manifold. It shows the existence of normal Fefferman constructions over CR and Lagrangian contact structures corresponding to holonomy reductions to SO(4,2) and SO(3,3), respectively. There is also a fascinating co…
New points detected on surfaces in 4D space, revealing symmetries.
Defines new structures on manifolds with symplectic properties.
Constructs geometries with nonvanishing curvature and essential automorphisms.
This paper analyses the parabolic geometries generated by a free -distribution in the tangent space of a manifold. It shows that certain holonomy reductions of the associated normal Tractor connections, imply preferred connections with special properties, along with Riemannian or sub-Riemannian structures on the man…
An elliptic complex is found on a Grassmannian space, with zero index.
The article constructs differential operators for parabolic geometries.
The study classifies points on ruled surfaces in 4-space based on geometric properties.