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

Author

Listed:
  • Young Ho Kim

    (Department of Mathematics, Kyungpook National University, Daegu 41566, Korea)

  • Sun Mi Jung

    (Department of Mathematics, Kyungpook National University, Daegu 41566, Korea)

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.

Suggested Citation

  • Young Ho Kim & Sun Mi Jung, 2020. "Spherical Ruled Surfaces in S 3 Characterized by the Spherical Gauss Map," Mathematics, MDPI, vol. 8(12), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2106-:d:450819
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