Projective Differential Geometry of Submanifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Projective Differential Geometry of Submanifolds write by M.A. Akivis. This book was released on 1993-06-30. Projective Differential Geometry of Submanifolds available in PDF, EPUB and Kindle. 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 studied: submanifolds carrying a net of conjugate lines (in particular, conjugate systems), tangentially degenerate submanifolds, submanifolds with asymptotic and conjugate distributions etc. The method of moving frames and the apparatus of exterior differential forms are systematically used in the book and the results presented can be applied to the problems dealing with the linear subspaces or their generalizations. Graduate students majoring in differential geometry will find this monograph of great interest, as will researchers in differential and algebraic geometry, complex analysis and theory of several complex variables.
Algebraic Geometry and Projective Differential Geometry
Algebraic Geometry and Projective Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry and Projective Differential Geometry write by J. M. Landsberg. This book was released on 1999. Algebraic Geometry and Projective Differential Geometry available in PDF, EPUB and Kindle.
Projective Differential Geometry Old and New
Projective Differential Geometry Old and New - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Projective Differential Geometry Old and New write by V. Ovsienko. This book was released on 2004-12-13. Projective Differential Geometry Old and New available in PDF, EPUB and Kindle. Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject.
Differential Geometry of Varieties with Degenerate Gauss Maps
Differential Geometry of Varieties with Degenerate Gauss Maps - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry of Varieties with Degenerate Gauss Maps write by Maks A. Akivis. This book was released on 2004. Differential Geometry of Varieties with Degenerate Gauss Maps available in PDF, EPUB and Kindle. This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate 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.
On the Geometry of Some Special Projective Varieties
On the Geometry of Some Special Projective Varieties - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On the Geometry of Some Special Projective Varieties write by Francesco Russo. This book was released on 2016-01-25. On the Geometry of Some Special Projective Varieties available in PDF, EPUB and Kindle. Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne’s Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern tools of Mori Theory and of rationally connected manifolds. The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once this embedded manifold, usually of lower codimension, is classified, one tries to reconstruct the original manifold, following a principle appearing also in other areas of geometry such as projective differential geometry or complex geometry.
