CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

A Classification of Three-dimensional Real Hypersurfaces in Non-flat Complex Space Forms in Terms of Their generalized Tanaka-Webster Lie Derivative

  Published:2016-08-19
 Printed: Dec 2016
  • George Kaimakamis,
    Faculty of Mathematics and Engineering Sciences, Hellenic Military Academy, Vari, Attiki, Greece
  • Konstantina Panagiotidou,
    Faculty of Mathematics and Engineering Sciences, Hellenic Military Academy, Vari, Attiki, Greece
  • Juan de Dios PĂ©rez,
    Departmento de Geometria y Topologia, Universidad de Granada, 18071, Granada Spain
Format:   LaTeX   MathJax   PDF  

Abstract

On a real hypersurface $M$ in a non-flat complex space form there exist the Levi-Civita and the k-th generalized Tanaka-Webster connections. The aim of the present paper is to study three dimensional real hypersurfaces in non-flat complex space forms, whose Lie derivative of the structure Jacobi operator with respect to the Levi-Civita connections coincides with the Lie derivative of it with respect to the k-th generalized Tanaka-Webster connection. The Lie derivatives are considered in direction of the structure vector field and in directions of any vecro field orthogonal to the structure vector field.
Keywords: $k$-th generalized Tanaka-Webster connection, non-flat complex space form, real hypersurface, Lie derivative, structure Jacobi operator $k$-th generalized Tanaka-Webster connection, non-flat complex space form, real hypersurface, Lie derivative, structure Jacobi operator
MSC Classifications: 53C15, 53B25 show english descriptions General geometric structures on manifolds (almost complex, almost product structures, etc.)
Local submanifolds [See also 53C40]
53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.)
53B25 - Local submanifolds [See also 53C40]
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/