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Geometriae Dedicata

, Volume 102, Issue 1, pp 143–150 | Cite as

Contact CR-Warped Product Submanifolds in Sasakian Manifolds

  • Izumi Hasegawa
  • Ion Mihai
Article

Abstract

Recently, B.-Y. Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain a sharp inequality for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Sasakian manifolds. The equality case is considered. Also, the minimum codimension of a contact CR-warped product in an odd-dimensional sphere is determined.

contact CR-submanifold Sasakian manifold Sasakian space form warped product 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Izumi Hasegawa
    • 1
  • Ion Mihai
    • 2
  1. 1.Department of MathematicsHokkaido University of EducationAinosato, Kita-ku, SapporoJapan
  2. 2.Faculty of MathematicsUniversity of BucharestBucharestRomania

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