On a Riemannian invariant of Chen type
Teodor Oprea
Abstract
In [6] 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 M(c), varying with c and the mean curvature of M in M(c). A improuvement of this inequality in the Lagrangian case is obtained.
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