Haesen, Stefan Optimal inequalities for embedded space-times. (English) Zbl 1119.53037 Kragujevac J. Math. 28, 69-85 (2005). The author considers the embedding of a Riemannian or Lorentzian manifold as a hypersurface into a semi-Riemannian space. He proves the inequality between intrinsic and extrinsic curvatures, namely between the \(\Lambda\)-curvatures of Chen and squared mean curvature. Moreover, he gives some examples and discusses its applications in higher-dimensional physics (Bianchi models, Kaluza–Klein models). Reviewer: Mirjana Đorić (Beograd) Cited in 2 Documents MSC: 53C40 Global submanifolds 53C80 Applications of global differential geometry to the sciences 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 83E15 Kaluza-Klein and other higher-dimensional theories Keywords:semi-Riemannian space; causal-type preserving embedding; \(\Lambda\)-curvatures of Chen; general relativity PDFBibTeX XMLCite \textit{S. Haesen}, Kragujevac J. Math. 28, 69--85 (2005; Zbl 1119.53037)