相关论文: 3-dimensional methods in contact geometry

This is an overview of merging the techniques of Riesz space theory and convex geometry.

It is provided an overview of existed results concerning classification of contact metric, almost cosymplectic and almost Kenmotsu $(\kappa,\mu)$-manifolds. In the case of dimension three it is described in full details structure of contact…

These notes were prepared for a series of intensive lectures delivered at Hokkaido University, Nagoya University, Kyoto University, and Kyushu University. We begin with a brief review of higher-form symmetries, anomalies, and discrete gauge…

This survey explores the geometry of three-dimensional Anosov flows from the perspective of contact and symplectic geometry, following the work of Mitsumatsu, Eliashberg-Thurston, Hozoori, and the author. We also present a few original…

This contribution presents a brief survey of clipping and intersection algorithms in E2 and E3 with a nearly complete list of relevant references. Some algorithms use the projective extension of the Euclidean space and vector-vector…

This paper applies the Newman-Penrose formalism-a technique primarily used in General Relativity-to the analysis of three-dimensional almost contact metric (ACM) manifolds. We reformulate and discuss several known notions and properties…

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We…

These notes are based on lectures given in Valencia in October 2008 and in Stockholm in November 2008, in the framework of the Nordita workshop "Geometrical aspects of String Theory". We introduce the notion of a metric 3-Lie algebra and…

These are the lecture notes for a short course on geometric quantization given by the author at the XVIII Modave Summer School on Mathematical Physics, Sep 5 - Sep 9.

The aim of our paper is to render an object in 3-dimension using a set of its orthographic views. Corner detector (Harris Detector) is applied on the input views to obtain control points. These control points are projected perpendicular to…

These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is…

Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…

We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.

This paper presents a multimodal framework that integrates touch signals (contact points and surface normals) into 3D Gaussian Splatting (3DGS). Our approach enhances scene reconstruction, particularly under challenging conditions like low…

In recent times a great amount of progress has been achieved in symplectic and contact geometry, leading to the development of powerful invariants of 3-manifolds such as Heegaard Floer homology and embedded contact homology. These…

The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art…

A height-function-based numerical approach is developed for enforcing contact angles on flat and curved solid surfaces within two-dimensional volume-of-fluid simulations. This method incorporates the contact line position into the curvature…

We classify Legendrian torus knots and figure eight knots in the tight contact structure on the 3-sphere up to Legendrian isotopy. As a corollary to this we also obtain the classification of transversal torus knots and figure eight knots up…

This work introduces a contact interaction methodology for an unbiased treatment of contacting surfaces without assigning surfaces as master and slave. The contact tractions between interacting discrete segments are evaluated with respect…

This is the text of a series of five lectures given by the author at the "Second Annual Spring Institute on Noncommutative Geometry and Operator Algebras" held at Vanderbilt University in May 2004. It is meant as an overview of recent…