Quadric surfaces of coordinate finite type Gauss map

Abstract

We study quadric surfaces in the 3-dimensional Euclidean space which are of coordinate finite type Gauss map with respect to the second fundamental form $II$, i.e., their Gauss map vector $\mathbf{n}$ satisfies the relation ${\Delta }^{II}\mathbf{n}=\Lambda \mathbf{n}$, where ${\Delta }^{II}$ denotes the Laplace operator of the second fundamental form $II$ of the surface and $\Lambda$ is a square matrix of order 3. We show that helicoids and spheres are the only class of surfaces mentioned above satisfying ${\Delta }^{II}\mathbf{n}=\Lambda \mathbf{n}$.

arXiv admin note: text overlap with arXiv:1610.05102

Cited by in corpus (1)

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