On Joachimsthal's theorems in semi-Euclidean spaces

Coken A. C., Gorgulu A.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.70, no.11, pp.3932-3942, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 11
  • Publication Date: 2009
  • Doi Number: 10.1016/j.na.2008.08.003
  • Journal Name: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3932-3942
  • Keywords: Semi-Euclidean spaces, Joachimsthal's theorems, Indefinite metric, Semi-Riemannian manifold, Semi-orthogonal group, Structure equations
  • Akdeniz University Affiliated: No

Abstract

In this work, we study Joachimsthal's theorems in semi-Euclidean spaces E-nu(n+1). We obtain a relation between the curvatures of the strips in semi-Euclidean spaces E-nu(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, nu = 0 and the original Joachimsthal theorem from our matrix equation in the case n = 2, nu = 1. (C) 2008 Elsevier Ltd. All rights reserved.