catenoid

However, the Laplacian of the Gauss map of several surfaces and hypersurfaces, such as catenoids and right cones in [E.sup.3] [10], generalized catenoids and right n-cones in [E.sup.n+1] [11], and helicoids of the 1st, 2nd, and 3rd kind, conjugate Enneper's surfaces of the second kind, and B-scrolls in [E.sub.1.sup.3] [16] take the form

For instance, when [alpha] = 0, the generalized catenoids of the first and the third kind have proper pointwise 1-type Gauss map of the first kind.

Hypersurfaces with pointwise 1-type Gauss map in Lorentz--Minkowski space/ Huperpinnad punktiti 1-tuupi Gaussi kujutusega Lorentzi-Minkowski ruumis