On a Riemannian invariant of Chen type (Q1011020)
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| Language | Label | Description | Also known as |
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| English | On a Riemannian invariant of Chen type |
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On a Riemannian invariant of Chen type (English)
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7 April 2009
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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 \(\widetilde{M}(c)\).
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