On Joachimsthal’s theorems in semi-Euclidean spaces

In this work, we study Joachimsthal’s theorems in semi-Euclidean spaces E ν n + 1 . We obtain a relation between the curvatures of the strips in semi-Euclidean spaces E ν n + 1 in matrix form depending on a semi-orthogonal matrix. This matrix equation gives us a generalization of the original Joachi...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear analysis 2009-06, Vol.70 (11), p.3932-3942
Main Authors: Coeken, A Ceylan, Goerguelue, Ali
Format: Article
Language:English
Subjects:
Indefinite metric
Joachimsthal’s theorems
Semi-Euclidean spaces
Semi-orthogonal group
Semi-Riemannian manifold
Structure equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this work, we study Joachimsthal’s theorems in semi-Euclidean spaces E ν n + 1 . We obtain a relation between the curvatures of the strips in semi-Euclidean spaces E ν n + 1 in matrix form depending on a semi-orthogonal matrix. This matrix equation gives us a generalization of the original Joachimsthal theorem in semi-Euclidean space E 1 3 and the well-known Joachimsthal theorem of the surface theory. In addition, we reobtain the well-known Joachimsthal theorem from our matrix equation in the case n = 2 , ν = 0 and the original Joachimsthal theorem from our matrix equation in the case n = 2 , ν = 1 .
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2008.08.003