J. Austral. Math. Soc.  72 (2002), 247-256
Ricci curvature of submanifolds in Sasakian space forms

Ion Mihai
  Faculty of Mathematics
  University of Bucharest
  Str. Academiei 14
  70109 Bucharest
  Romania
  imihai@math.math.unibuc.ro


Abstract
Recently, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Afterwards, we dealt with similar problems for submanifolds in complex space forms. In the present paper, we obtain sharp inequalities between the Ricci curvature and the squared mean curvature for submanifolds in Sasakian space forms. Also, estimates of the scalar curvature and the k-Ricci curvature respectively, in terms of the squared mean curvature, are proved.
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