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Sasakian geometry, hypersurface singularities, and Einstein metrics. (English) Zbl 1101.53023
Slovák, Jan (ed.) et al., The proceedings of the 24th winter school “Geometry and physics”, Srní, Czech Republic, January 17–24, 2004. Palermo: Circolo Matemático di Palermo. Supplemento ai Rendiconti del Circolo Matemático di Palermo. Serie II 75, 57-87 (2005).
This is a survey article on Sasakian geometry which has emerged as one of the most powerful tools of constructing and proving existence of special Riemannian metrics, such as Einstein metrics or metrics of positive Ricci curvature on a wide range of odd-dimensional manifolds. The key geometric object in the theory is that of a contact structure (hence only odd dimensions) together with a Riemannian metric naturally adapted to the contact form.
For the entire collection see [Zbl 1074.53001].

MSC:
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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