Differential Geometry Of Submanifolds PDF Download
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Author | : Bang-yen Chen |
Publisher | : World Scientific |
Total Pages | : 517 |
Release | : 2017-05-29 |
Genre | : Mathematics |
ISBN | : 9813208945 |
Download Differential Geometry Of Warped Product Manifolds And Submanifolds Book in PDF, ePub and Kindle
A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson-Walker models, are warped product manifolds.The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson-Walker's and Schwarzschild's.The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century.The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.
Author | : Maks A. Akivis |
Publisher | : Springer Science & Business Media |
Total Pages | : 272 |
Release | : 2006-04-18 |
Genre | : Mathematics |
ISBN | : 0387215115 |
Download Differential Geometry of Varieties with Degenerate Gauss Maps Book 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.
Author | : M.A. Akivis |
Publisher | : Elsevier |
Total Pages | : 375 |
Release | : 1993-06-30 |
Genre | : Mathematics |
ISBN | : 0080887163 |
Download Projective Differential Geometry of Submanifolds Book 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.
Author | : Bang-Yen Chen |
Publisher | : Courier Dover Publications |
Total Pages | : 193 |
Release | : 2019-06-12 |
Genre | : Mathematics |
ISBN | : 0486832783 |
Download Geometry of Submanifolds Book in PDF, ePub and Kindle
The first two chapters of this frequently cited reference provide background material in Riemannian geometry and the theory of submanifolds. Subsequent chapters explore minimal submanifolds, submanifolds with parallel mean curvature vector, conformally flat manifolds, and umbilical manifolds. The final chapter discusses geometric inequalities of submanifolds, results in Morse theory and their applications, and total mean curvature of a submanifold. Suitable for graduate students and mathematicians in the area of classical and modern differential geometries, the treatment is largely self-contained. Problems sets conclude each chapter, and an extensive bibliography provides background for students wishing to conduct further research in this area. This new edition includes the author's corrections.
Author | : Krishan L. Duggal |
Publisher | : Springer Science & Business Media |
Total Pages | : 484 |
Release | : 2011-02-02 |
Genre | : Mathematics |
ISBN | : 3034602510 |
Download Differential Geometry of Lightlike Submanifolds Book in PDF, ePub and Kindle
This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kählerian, Sasakian and quaternion Kähler manifolds.
Author | : K. Kenmotsu |
Publisher | : Springer |
Total Pages | : 138 |
Release | : 2007-01-05 |
Genre | : Mathematics |
ISBN | : 3540390650 |
Download Differential Geometry of Submanifolds Book in PDF, ePub and Kindle
Author | : IUrii Akhmetovich Aminov |
Publisher | : |
Total Pages | : 126 |
Release | : 2000 |
Genre | : Geometry, Differential |
ISBN | : |
Download New Ideas in Differential Geometry of Submanifolds Book in PDF, ePub and Kindle
Author | : Luc Vrancken |
Publisher | : Lulu.com |
Total Pages | : 266 |
Release | : 2008-06-30 |
Genre | : Mathematics |
ISBN | : 1847990169 |
Download Symposium on the Differential Geometry of Submanifolds Book in PDF, ePub and Kindle
This book contains the proceedings of the «Symposium on differential geometry» which took place at the Université de Valenciennes et du Hainaut Cambrésis from July 3, 2007 until July 7, 2007.The main theme of the conference was the differential geometry of submanifolds. Special emphasis was put on the following topics:Lagrangian immersions, Minimal immersions and constant mean curvature immersions, Harmonic maps and harmonic morphisms, Variational problems, Affine differential geometry. This conference follows the tradition of the conferences in the series of « Geometry and Topology of Submanifolds », which started with the Luminy meeting in 1987 and then continued with various meetings at different places in Europe, such as amongst others Avignon, Leeds, Leuven, Brussels, Nordfjordeid, Berlin, Warszawa, Bedlewo and also in China (Beijing, 1998).
Author | : Sadahiro Maeda |
Publisher | : World Scientific |
Total Pages | : 308 |
Release | : 2013-10-23 |
Genre | : Mathematics |
ISBN | : 9814566292 |
Download Differential Geometry Of Submanifolds And Its Related Topics - Proceedings Of The International Workshop In Honor Of S Maeda's 60th Birthday Book in PDF, ePub and Kindle
This volume is a compilation of papers presented at the conference on differential geometry, in particular, minimal surfaces, real hypersurfaces of a non-flat complex space form, submanifolds of symmetric spaces and curve theory. It also contains new results or brief surveys in these areas. This volume provides fundamental knowledge to readers (such as differential geometers) who are interested in the theory of real hypersurfaces in a non-flat complex space form.
Author | : Barbara Opozda |
Publisher | : |
Total Pages | : 76 |
Release | : 1992 |
Genre | : Geometry, Differential |
ISBN | : |
Download Some Contributions to the Differential Geometry of Submanifolds Book in PDF, ePub and Kindle