Recognizable classification of Lorentzian distance-squared mappings

Abstract

The Lorentzian length, which is one of the most significant functions in Lorentzian geometry, is a complex-valued function. Its square gives a real-valued non-degenerate quadratic function. In this paper, we define naturally extended mappings of Lorentzian distance-squared functions, wherein each component is a Lorentzian distance-squared function; and classify these mappings completely by the likeness of recognition subspaces.

Cited by in corpus (6)

• Generic linear perturbations
• Around distance-squared mappings
• Generalized distance-squared mappings of the plane into the plane
• Geometric interpretation of generalized distance-squared mappings of ${\mathbb{R}}^2$ into ${\mathbb{R}}^{\ell }$ $(\ell \ge 3)$
• Composing generic linearly perturbed mappings and immersions/injections
• Stability of $C^{\infty }$ convex integrands