Geometric Theory of Foliations

by Thomas E. Cecil (Author), Patrick J. Ryan (Author)
Presents thorough treatment of hypersurfaces in real, complex, and quaternionic space forms with connections to symmetric spaces, homogeneous spaces, and Riemannian geometry
Treats Dupin hypersurfaces using both standard and Lie sphere geometric techniques
Discusses the comprehensive treatment of the theory of isoparametric hypersurfaces due to Cartan and Münzner that are necessary for understanding the subject

Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds. The school consisted of four courses, focusing on both the construction of non-Kähler manifolds and the understanding of a possible classification of complex non-Kähler manifolds. In particular, the courses by Alberto Verjovsky and Andrei Teleman introduced tools in the theory of foliations and analytic techniques for the classification of compact complex surfaces and compact Kähler manifolds, respectively. The courses by Sebastien Picard and Sławomir Dinew focused on analytic techniques in Hermitian geometry, more precisely, on special Hermitian metrics and geometric flows, and on pluripotential theory in complex non-Kähler geometry.