Decomposition of derivatives and compatibility conditions
type: Item
instance of: scholarly article
title: Decomposition of derivatives and compatibility conditions
zbMATH Open document ID: 0869.53011
DOI: 10.1016/0393-0440(95)00058-5
author: Gianluca Gemelli
published in: Journal of Geometry and Physics
publication date: 1996-12-01T00:00:00Z
review text: Along a hypersurface \(\{x\in V_{N+1} |f(x)= 0\}\) in an \((N+1)\)-dimensional manifold \(V_{N+1}\), partial derivatives and covariant derivatives can be decomposed into ``inner derivatives'' (tangent to the hypersurface) and ``exterior derivatives'' (transverse to the hypersurface). In this paper a special scheme is presented that allows to perform this decomposition for arbitrarily high derivatives of tensor fields in a noniterative manner. The resulting formulae are particularly useful for the formulation of jump conditions of tensor fields which are regularly discontinuous along a hypersurface.
reviewed by: Volker Perlick
Mathematics Subject Classification ID: 53A45
Mathematics Subject Classification ID: 53Z05
zbMATH DE Number: 951816
zbMATH Keywords: derivatives of tensor fields
zbMATH Keywords: jump conditions
MaRDI profile type: Publication
full work available at URL: 0393-0440(95)00058-5
OpenAlex ID: W2067266297
cites work: Q3694227
cites work: Relativistic Fluids and Magneto-fluids
cites work: Q4325518
cites work: Q5530901
cites work: Q3871536
cites work: Q4749299
cites work: Q4146306
cites work: The dynamics of discontinuity surfaces in general relativity theory
cites work: Applications of Distributional Derivatives to Wave Propagation
cites work: Q4076197
cites work: Propagateurs et commutateurs en relativité générale
cites work: Ondes de choc et hypothèses de compressibilité en magnétohydrodynamique relativiste
cites work: Q4084336
cites work: Q5812941
cites work: Ricci-Calculus
cites work: Q3242668
cites work: Hypersurfaces in Einstein-Riemann space and their compatibility conditions
description: scientific article; zbMATH DE number 951816