In this book the authors study the differential geometry of varieties with degenerate Gauss maps. They use the main methods of differential geometry, namely, the methods of moving frames and exterior differential forms as well as tensor methods. By means of these methods, the authors discover the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.

The authors introduce the above mentioned methods and apply them to a series of concrete...

In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are...

Conformal differential geometry plays an important role in many areas of differential geometry and other fields of mathematics. Since the late 1800s, various developments in this field have occurred. The main notions discussed in the book include the importance of surfaces with isometric or spherical curvature lines, canal surfaces, congruence of circles, and three-orthogonal systems of surface.

Devoted to the geometry of multi-dimensional three-webs, this monograph presents the classical and more recent results of the theory, and those parts of geometry and algebra which are closely connected with it. Many problems of the theory of smooth quasigroups and loops are considered. In addition to the general theory of webs, important classes of special webs are also studied.