Oprea, Teodor Optimization methods on Riemannian submanifolds. (English) Zbl 1150.53340 An. Univ. Bucur., Mat. 54, No. 1, 127-136 (2005). 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. Cited in 2 ReviewsCited in 15 Documents MSC: 53C40 Global submanifolds 90-XX Operations research, mathematical programming Keywords:optimization methods; programming problems; sectional curvature; Chen inequality PDFBibTeX XMLCite \textit{T. Oprea}, An. Univ. Bucur., Mat. 54, No. 1, 127--136 (2005; Zbl 1150.53340)