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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.)
Citations:
Zbl 1150.53340
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References:
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