ON A RIEMANNIAN INVARIANT OF CHEN TYPE

ON A RIEMANNIAN INVARIANT OF CHEN TYPE

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 submanifol...

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Veröffentlicht in:The Rocky Mountain journal of mathematics 2008-01, Vol.38 (2), p.567-581
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Curvature
Lagrangian function
Mathematical vectors
Optimal solutions
Partial derivatives
Riemann manifold
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description 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 M͠(c), varying with and the mean curvature of M in M͠(c).
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subjects Curvature
Lagrangian function
Mathematical vectors
Optimal solutions
Partial derivatives
Riemann manifold
title ON A RIEMANNIAN INVARIANT OF CHEN TYPE
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