An inequality between intrinsic and extrinsic scalar curvature invariants for codimension 2 embeddings
type: Item
instance of: scholarly article
title: An inequality between intrinsic and extrinsic scalar curvature invariants for codimension 2 embeddings
zbMATH Open document ID: 1083.53062
author: Stefan Haesen
author: Miroslava Petrović-Torgasěv
author: Leopold Verstraelen
author: Franki Dillen
published in: Journal of Geometry and Physics
publication date: 2005-06-13T00:00:00Z
review text: In this paper, the authors study the local and isometric embedding of an \(m\)-dimensional Lorentzian manifold in an \((m+2)\)-dimensional pseudo-Euclidean space. An inequality is proved between the basic curvature invariants, i.e., the intrinsic scalar curvature and the extrinsic mean and scalar normal curvature. The inequality becomes an equality if two components of the second fundamental form have a specified form with respect to some orthonormal basis of the manifold. As an application, one can look at the space-times embedded in a six-dimensional pseudo-Euclidean space for which the equality holds. They turn out to be Petrov type D models filled with an anisotropic perfect fluid and containing a timelike two-surface of constant curvature.
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 2175247
zbMATH Keywords: embedding
zbMATH Keywords: codimension 2 normal curvature
MaRDI profile type: Publication
full work available at URL: j.geomphys.2004.02.003
OpenAlex ID: W2042492541
cites work: Isometric embedding of BPS branes in flat spaces with two times
cites work: Q4934908
cites work: Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
cites work: The embedding of space–times in five dimensions with nondegenerate Ricci tensor
cites work: The embedding of the space–time in five dimensions: An extension of the Campbell–Magaard theorem
cites work: Q4814455
cites work: Isometric Embedding of Riemannian Manifolds into Euclidean Spaces
cites work: Q3322013
cites work: Normal curvature of surfaces in space forms
cites work: Ideally embedded space–times
cites work: The Large Scale Structure of Space-Time
cites work: Petrov type \(D\) Einstein space-times of embedding class two.
cites work: The twisting connection of space–time
cites work: Q5562586
cites work: Large Mass Hierarchy from a Small Extra Dimension
cites work: An Alternative to Compactification
cites work: Exact Solutions of Einstein's Field Equations
cites work: Vacuum solutions of embedding class 2: Petrov types D and N
cites work: Q4266061
DOI: 10.1016/J.GEOMPHYS.2004.02.003
description: scientific article; zbMATH DE number 2175247