Spherical Ruled Surfaces in S 3 Characterized by the Spherical Gauss Map

Young Ho Kim and Sun Mi Jung
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Young Ho Kim: Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
Sun Mi Jung: Department of Mathematics, Kyungpook National University, Daegu 41566, Korea

Mathematics, 2020, vol. 8, issue 12, 1-14

Abstract: The Laplace operator on a Riemannian manifold plays an important role with eigenvalue problems and the spectral theory. Extending such an eigenvalue problem of smooth maps including the Gauss map, the notion of finite-type was introduced. The simplest finite-type is of 1-type. In particular, the spherical Gauss map is defined in a very natural way on spherical submanifolds. In this paper, we study ruled surfaces of the 3-dimensional sphere with generalized 1-type spherical Gauss map which generalizes the notion of 1-type. The classification theorem of ruled surfaces of the sphere with the spherical Gauss map of generalized 1-type is completed.

Keywords: Laplace operator; spherical Gauss map; pointwise 1-type; generalized 1-type (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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