Lorentzian Beltrami-Euler formula and generalized Lorentzian Lamarle formila in R_1^n

Abstract

In this paper, the sectional curvature of non-degenerate tangent sections of time-like ruled surface with the central ruled surface in n-dimensional Minkowski space, R_1^n is studied. The relationship between normal sectional curvature and the principal sectional curvatures of non-degenerate tangent sections of time-like ruled surfaces is obtained andcalled as Lorentzian Beltrami-Euler formula. Moreover, the relationship between the Gaussian curvature and the principal distribution parameter of the non-degenerate tangent sections of time-like ruled surfaces is obtained and called as generalized Lorentzian Lamarle formula.

Keywords

• Sectional curvature
• Ruled surface
• Beltrami-Euler formula
• Lamarle formula