Singular spaces from special holonomy and foliations

Spaces with singularities naturally appear in differential geometry and mathematical physics. The project is based on and further develops our research results reached in the following topics: the holonomy groups of cones over pseudo-Riemannian manifolds, their relations to Lorentzian manifold admitting imaginary Killing spinors, Sasakian and other special geometries, constructions of new examples of complete G2 and Spin(7)-holonomy metrics and study of their deformations, constructions of invariant Kaehler-Einstein and Einstein-Sasakian metrics on cohomogeneity one manifolds. We also plan to investigate the geometry of the leaf space of foliations and, in particular, to develop Losik's approach to these spaces and to study their characteristic classes.