Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 1998; 35(2): 315-330

Printed June 1, 1998

Copyright © The Korean Mathematical Society.

Space-like surfaces with 1-type generalized Gauss map

Soon Meen Choi, U-Hang Ki, and Young Jin Suh

Kyungpook National University, Kyungpook National University and Kyungpook National University

Abstract

Chen and Piccinni [7] have classified all compact surfaces in a Euclidean space $\text{\bf R}^{2+p}$ with 1-type generalized Gauss map. Being motivated by this result, the purpose of this paper is to consider the Lorentz version of the classification theorem and to obtain a complete classification of space-like surfaces in indefinite Euclidean space $\text{\bf R}_p^{2+p}$ with 1-type generalized Gauss map.

Keywords: space-like surfaces, Gauss map, 1-type generalized Gauss map, totally umbilical hypersurface, Grassmann manifold

MSC numbers: Primary 53C40, Secondary 53C15