An improved Chen–Ricci inequality for special slant submanifolds in Kenmotsu space forms
Tom 110 / 2014
Annales Polonici Mathematici 110 (2014), 81-89 MSC: Primary 53C40; Secondary 53C15, 53C25. DOI: 10.4064/ap110-1-7
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.