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Optimization methods on Riemannian submanifolds. (English) Zbl 1150.53340

Summary: We study the type of constrained programming problems: \[ \underset{x\in M}\min f(x), \] where \((N,\Tilde g)\) denote an \(m\)-dimensional Riemannian manifold, \(M\) a Riemannian submanifold in \(N,g\) the metric tensor induced by \(\Tilde g\) on \(M\) and \(f:N\to\mathbb{R}\) a smooth function. The result obtained is used in some Riemannian problems like the study of the distance between two manifolds, of the extremes of sectional curvature and is applied successfully in the proof of the Chen inequality.

MSC:

53C40 Global submanifolds
90-XX Operations research, mathematical programming
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