Surfaces in the complexified sphere parametrized by a complex orthogonal net

Access this Article

Search this Article

Abstract

We study surfaces in the complexified sphere parameterized by a complex orthogonal net and show that the fundamental theorem of these surfaces is stated in terms of two functions called the curvatures. We also exhibit fundamental examples by assuming natural conditions on the curvatures, which include a portion of the sphere, the hyperboloid of one sheet or the hyperboloid of two sheets, and the surfaces whose integrability condition is given by the complexified Liouville's equation.

Journal

  • JP journal of geometry and topology

    JP journal of geometry and topology 10(2), 89-181, 2010-07

    Pushpa Publishing House

Codes

  • NII Article ID (NAID)
    120004205532
  • NII NACSIS-CAT ID (NCID)
    AA11927388
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0972-415X
  • Data Source
    IR 
Page Top