Gürses, Metin Sigma models, minimal surfaces and some Ricci flat pseudo-Riemannian geometries. (English) Zbl 1070.53503 Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 2nd international conference on geometry, integrability and quantization, Varna, Bulgaria, June 7–15, 2000. Sofia: Coral Press Scientific Publishing (ISBN 954-90618-2-5/pbk). 171-180 (2001). Summary: We consider the sigma models where the base metric is proportional to the metric of the configuration space. We show that the corresponding sigma model equation admits a Lax pair. We also show that this type of sigma models in two dimensions are intimately related to the minimal surfaces in a flat pseudo-Riemannian 3-space. We define two dimensional surfaces conformally related to the minimal surfaces in flat three dimensional geometries which enable us to give a construction of the metrics of some even dimensional Ricci flat (pseudo-) Riemannian geometries.For the entire collection see [Zbl 0957.00038]. MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53B30 Local differential geometry of Lorentz metrics, indefinite metrics Keywords:minimal surfaces; pseudo-Riemannian 3-space; Ricci flat PDFBibTeX XMLCite \textit{M. Gürses}, in: Proceedings of the 2nd international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 7--15, 2000. Sofia: Coral Press Scientific Publishing. 171--180 (2001; Zbl 1070.53503) Full Text: arXiv