# Extension of Eigenvalue Problems on Gauss Map of Ruled Surfaces

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## Abstract

**:**

## 1. Introduction

**Definition**

**1.**

**Example**

**1**

**([15]).**Let M be a surface in ${\mathbb{E}}^{3}$ parameterized by

**Definition**

**2**

**([15]).**The Gauss map G of a submanifold M in ${\mathbb{E}}^{m}$ is of generalized 1-type if the Gauss map G of M satisfies

**Definition**

**3.**

**Remark**

**1**

## 2. Preliminaries

## 3. Cylindrical Ruled Surfaces in ${\mathbb{E}}^{\mathbf{3}}$ with Generalized 1-Type Gauss Map

## 4. Classification Theorem

**Remark**

**2.**

**Theorem**

**2.**

**Proof.**

**Theorem**

**3.**

**Theorem**

**4.**

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Choi, M.; Kim, Y.H. Extension of Eigenvalue Problems on Gauss Map of Ruled Surfaces. *Symmetry* **2018**, *10*, 514.
https://doi.org/10.3390/sym10100514

**AMA Style**

Choi M, Kim YH. Extension of Eigenvalue Problems on Gauss Map of Ruled Surfaces. *Symmetry*. 2018; 10(10):514.
https://doi.org/10.3390/sym10100514

**Chicago/Turabian Style**

Choi, Miekyung, and Young Ho Kim. 2018. "Extension of Eigenvalue Problems on Gauss Map of Ruled Surfaces" *Symmetry* 10, no. 10: 514.
https://doi.org/10.3390/sym10100514