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On a Riemannian invariant of Chen type. (English) Zbl 1195.53072
In [An. Univ. Bucur., Mat. 54, No. 1, 127–136 (2005; Zbl 1150.53340)] we proved Chen’s inequality regarded as a problem of constrained maximum. In this paper we introduce a Riemannian invariant obtained from Chen’s invariant, replacing the sectional curvature by the Ricci curvature of $$k$$-order. This invariant can be estimated, in the case of submanifolds $$M$$ in space forms $$\widetilde{M}(c)$$, varying with $$c$$ and the mean curvature of $$M$$ in $$\widetilde{M}(c)$$.

##### MSC:
 53C40 Global submanifolds 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
Zbl 1150.53340
Full Text:
##### References:
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