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Extension of Eigenvalue Problems on Gauss Map of Ruled Surfaces

1
Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Korea
2
Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
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Author to whom correspondence should be addressed.
Symmetry 2018, 10(10), 514; https://doi.org/10.3390/sym10100514
Received: 20 September 2018 / Revised: 9 October 2018 / Accepted: 12 October 2018 / Published: 16 October 2018
A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from the eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of 1-type in the usual sense and pointwise 1-type. We classify ruled surfaces with a 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. View Full-Text
Keywords: ruled surface; pointwise 1-type Gauss map; generalized 1-type Gauss map; conical surface of G-type ruled surface; pointwise 1-type Gauss map; generalized 1-type Gauss map; conical surface of G-type
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 H. Kim. 2018. "Extension of Eigenvalue Problems on Gauss Map of Ruled Surfaces" Symmetry 10, no. 10: 514. https://doi.org/10.3390/sym10100514

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