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An improved Chen–Ricci inequality for special slant submanifolds in Kenmotsu space forms

Volume 110 / 2014

Simona Costache, Iuliana Zamfir Annales Polonici Mathematici 110 (2014), 81-89 MSC: Primary 53C40; Secondary 53C15, 53C25. DOI: 10.4064/ap110-1-7

Abstract

B. Y. Chen [Arch. Math. (Basel) 74 (2000), 154–160] proved a geometrical inequality for Lagrangian submanifolds in complex space forms in terms of the Ricci curvature and the squared mean curvature. Recently, this Chen–Ricci inequality was improved in [Int. Electron. J. Geom. 2 (2009), 39–45].

On the other hand, K. Arslan et al. [Int. J. Math. Math. Sci. 29 (2002), 719–726] established a Chen–Ricci inequality for submanifolds, in particular in contact slant submanifolds, in Kenmotsu space forms.

In this article, we improve the latter inequality for special slant submanifolds in Kenmotsu space forms. We also investigate the equality case.

Authors

  • Simona CostacheDepartment of Mathematics
    University of Bucharest
    Str. Academiei 14
    010014 Bucureşti, Romania
    e-mail
  • Iuliana ZamfirDepartment of Mathematics
    University of Bucharest
    Str. Academiei 14
    010014 Bucureşti, Romania
    e-mail

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