Some applications of Cartan's theory on three-dimensional Cauchy-Riemann geometry
In part I, we show that in \(\mathbb{C}^ 2\), every nondegenerate real hypersurface with hermitian shape operator is, in fact, locally \(CR\)- equivalent to the unit sphere. In part II, surface area elements invariant under ambient \(CR\) transformations are constructed. Also an invariant Lorentzian metric on the surface is obtained. We deduce the equation of minimal surfaces with respect to the simplest invariant area element. Besides, we also carry out the actual computation for surfaces in the Heisenberg group.
scientific article; zbMATH DE number 784087