Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Extension of eigenvalue problems on Gauss map of ruled surfaces

Version 1 : Received: 20 September 2018 / Approved: 20 September 2018 / Online: 20 September 2018 (11:01:16 CEST)

A peer-reviewed article of this Preprint also exists.

Choi, M.; Kim, Y.H. Extension of Eigenvalue Problems on Gauss Map of Ruled Surfaces. Symmetry 2018, 10, 514. Choi, M.; Kim, Y.H. Extension of Eigenvalue Problems on Gauss Map of Ruled Surfaces. Symmetry 2018, 10, 514.

Journal reference: Symmetry 2018, 10, 514
DOI: 10.3390/sym10100514

## Abstract

A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of those of 1-type in the usual sense and pointwise 1-type. We classify ruled surfaces with generalized 1-type Gauss map as part of a plane, a circular cylinder, a cylinder over a base curve of an infinite type, a helicoid, a right cone and a conical surface of $G$-type.

## Keywords

ruled surface,;pointwise $1$-type Gauss map; generalized $1$-type Gauss map; conical surface of $G$-type

## Subject

MATHEMATICS & COMPUTER SCIENCE, Geometry & Topology

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