Results 171 to 180 of about 2,097,491 (204)

Cartan Connections and Kawaguchi Geometry of Spaces Obtained by the Moving Frame Method

Journal of Mathematical Sciences, 1998
The author gives a detailed quasi-complete review of Kawaguchi geometry of spaces obtained by the moving frame method, studied by himself in various previous papers. The review contains the main results concerning the geometry of the general type of Kawaguchi spaces together with their theoretical justification.
L. E. Evtushik
exaly   +3 more sources

On Backlund transformation and motion of null Cartan curves [PDF]

International Journal of Geometric Methods in Modern Physics (IJGMMP), 2021
The main scope of this paper is to examine null Cartan curves especially the ones with constant torsion. In accordance with this scope, the position vector of a null Cartan curve is stated by a linear combination of the vector fields of its pseudo ...
M. Erdoğdu, A. Yavuz
semanticscholar   +2 more sources

Dual Cartan Numbers and Pseudo-Null Lines

Mathematical Methods in the Applied Sciences
The study aims to introduce some geometric properties of dual Cartan numbers. Since a unit timelike Cartan number with lightlike vector part corresponds to a parabolic rotation around a lightlike axis, it has been shown that the unit dual Cartan number ...
Iskender Öztürk
exaly   +2 more sources

The variation of the electric field along optic fiber for null Cartan and pseudo-null frames

International Journal of Geometric Methods in Modern Physics, 2021
In this paper, we introduce new frame and new transformation associated with combined Korteweg–de Vries–modified Korteweg–de Vries (KdV–mKdV) equation, the mKdV and the KdV equations with respect to the null Cartan frame in Minkowski 3-space.
Nevin Ertuğ Gürbüz
semanticscholar   +5 more sources

Polyakov Soldering and Second-Order Frames: The Role of the Cartan Connection [PDF]

Letters in Mathematical Physics, 2008
Accept\'e pour publication dans Lett.
Serge Lazzarini
exaly   +4 more sources

Locally Inertial Reference Frames in Lorentzian and Riemann-Cartan Spacetimes [PDF]

Annalen Der Physik, 2012
AbstractIn this paper the concept of locally inertial reference frames (LIRFs) in Lorentzian and Riemann‐Cartan spacetime structures is scrutinized. A rigorous mathematical definition of a LIRF in both structures is given, something that needs preliminary a clear mathematical distinction between the concepts of observers, reference frames, naturally ...
W A Rodrigues
exaly   +3 more sources

Riemannian Geometry In An Orthogonal Frame

, 2001
Foreword by S S Chern. In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds.
É. Cartan
semanticscholar   +2 more sources

Finslerian structures: The Cartan–Clifton method of the moving frame

Journal of Mathematical Physics, 1993
A theory of Finslerian structures is presented using an unpublished method of Clifton. It consists of using Cartan’s moving frame method with fields of special bases, and the Cartan calculus of tensor-valued forms with nonredundant coordinates on sphere bundles (which are the base spaces of the Finsler bundles).
J. G. Vargas, D. Torr
semanticscholar   +2 more sources

A Novel Four-Field Mixed FE Approximation for Kirchhoff Rods Using Cartan’s Moving Frames

Computer Methods in Applied Mechanics and Engineering, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Debasish Roy, Junuthula N. Reddy
exaly   +3 more sources

Cartan Moving Frames and the Data Manifolds

Information Geometry
The purpose of this paper is to employ the language of Cartan moving frames to study the geometry of the data manifolds and its Riemannian structure, via the data information metric and its curvature at data points. Using this framework and through experiments, explanations on the response of a neural network are given by pointing out the output ...
Rita Fioresi, Stéphane Puechmorel
exaly   +3 more sources