The Space-like Surfaces with Vanishing Conformal Form in the Conformal Space

TL;DR

This paper classifies space-like surfaces in conformal space with vanishing conformal form, advancing understanding of their geometric properties within conformal geometry.

Contribution

It provides a classification of space-like surfaces with vanishing conformal form in conformal space up to conformal equivalence, a novel result in conformal geometry.

Findings

Complete classification of space-like surfaces with vanishing conformal form

Identification of conformal invariants for these surfaces

Extension of conformal geometry theory in $ extbf{Q}^n_1$

Abstract

The conformal geometry of surfaces in the conformal space $\mathbf Q^n_1$ is studied. We classify the space-like surfaces in $\mathbf Q^n_1$ with vanishing conformal form up to conformal equivalence.