... Nachbin, F.P. Peterson, I.M. Singer and A.C. Zaanen VOLUME 49 NORTH- HOLLAND AMSTERDAM • LONDON • NEW YORK • TOKYO Geometry of Submanifolds M.A. AKIVIS Moscow Institute of Steel and North-Holland Mathematical Library.

Author: M.A. Akivis

Publisher: Elsevier

ISBN: 0080887163

Category: Mathematics

Page: 361

View: 185

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.

The Geometry of Solitons : AARMS-CRM Workshop, June 4-9, 1999, Halifax, N.S.
, Canada A. A. Coley ... 1748-1794. 3. M. A. Akivis and V. V. Goldberg, Projective differential geometry of submanifolds, North- Holland Mathematical Library, vol.

Author: A. A. Coley

Publisher: American Mathematical Soc.

ISBN: 0821870254

Category: Mathematics

Page: 436

View: 688

This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. The book consists of two parts. The first is a series of introductory pedagogical lectures presented by leading experts in the field. They are devoted respectively to Backlund transformations of Painleve equations, to the dressing methodand Backlund and Darboux transformations, and to the classical geometry of Backlund transformations and their applications to soliton theory. The second part contains original contributions that represent new developments in the theory and applications of these transformations. Both the introductorylectures and the original talks were presented at an International Workshop that took place in Halifax, Nova Scotia (Canada). This volume covers virtually all recent developments in the theory and applications of Backlund and Darboux transformations.

... Projective Differential Geometry of Submanifolds, Math. Library 49, North- Holland ( 1 993). (329) [7| M.S. Alber, R. Camassa, D.D. Holm and J.E. Marsden,
The geometry of peaked solutions of a class of integrable pdes. Lett. Math. Phys.
32.

Author: C. Rogers

Publisher: Cambridge University Press

ISBN: 0521012880

Category: Mathematics

Page: 413

View: 893

This book explores the deep and fascinating connections that exist between a ubiquitous class of physically important waves known as solitons and the theory of transformations of a privileged class of surfaces as they were studied by eminent geometers of the nineteenth century. Thus, nonlinear equations governing soliton propagation and also mathematical descriptions of their remarkable interaction properties are shown to arise naturally out of the classical differential geometry of surfaces and what are termed Bäcklund-Darboux transformations.This text, the first of its kind, is written in a straightforward manner and is punctuated by exercises to test the understanding of the reader. It is suitable for use in higher undergraduate or graduate level courses directed at applied mathematicians or mathematical physics.

... Projective differential geometry of subman- ifolds, North-Holland Mathematical Library, 49, North-Holland Publishing ... [4] M. Bruck, X. Du, J. Park, and C.-L.
Terng, Submanifold geometry of real Grassmannian systems, The Memoirs, Vol.

Author: Michael Eastwood

Publisher: Springer Science & Business Media

ISBN: 0387738312

Category: Mathematics

Page: 568

View: 925

This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.

2. Akivis, M.A. and Goldberg, V.V., Projective Differential Geometry of Submanifolds, Amsterdam: North Holland, 1993 (North-Holland Math. Library, vol
. 49). 3. Anderson, I.M. and Kamran, N., The Variational Bicomplex for Second
Order Scalar ...

Author: American Mathematical SocietyPublish On: 1993

Projective. Differential. Geometry. of. Submanifolds By M.A. Akivis and V.V.
Goldberg North-Holland Mathematical Library Volume 49 1993.374 pages Price:
Dfl. 225.00 (US$ 128.50) ISBN 0-444-89771-2 In this book, the general theory of
...

60 3 – 30 [ 2 ] Agafonov S I and Ferapontov E V 1999 J . Math . Sci . 94 1748 - 92
[ 3 ] Akivis M A and Goldberg V V 1993 Projective Differential Geometry of Submanifolds ( Mathematics Library ) vol 49 ( Amsterdam : North - Holland ) [ 4 ]
Doliva ...

Proceedings of the Japan-United States Seminar on Minimal Submanifolds,
Including Geodesics, Tokyo 1977 Morio Obata ... [ 2 ] Cheeger , J . and Ebin , D . :
Comparison theorems in riemannian geometry , North - Holland Mathematical Library , 9 ... K . : Geodesic and curvature structures characterizing projective
spaces , Differential Geometry , in honor of K . Yano , Kinokuniya , Tokyo , 1972 ,
305 - 315 .

References of Play [ 1 ] J . BERNDT : Riemannian Geometry of Complex Two -
plane Grassmannians , Rend . Sem . ... D . EBIN : Comparison Theorems in
Riemannian Geometry , 1975 North Holland Publishing Mathematical Library Vol
. 9 . [ 5 ] B . Y . CHEN , T . NAGANO : Totally Geodesic Submanifolds of
Symmetric Spaces , II , Duke Mathematical Journal , Vol . ... C . U . SÁNCHEZ :
Maximal Projective Subspaces in the Variety of Planar Normal Sections of a Flag
Manifold , Geom .

J. Cheeger and D. Ebin , Comparison theorems in Riemannian geometry , North - Holland Mathematical Library , Amsterdam , 1975 . 5. J. Cheeger and ... 7. R. E.
Greene and H. Wu , Integrals of subharmonic functions on manifolds of
nonnegative curvature , Invent . Math . ... H. Nakagawa and K. Shiohama ,
Geodesic and curvature structures characterizing projective spaces , Diff . ... K.
Shiohama , The diameter of d - pinched manifolds , J. Differential Geometry , 5 (
1971 ) , 61–74 . 17 .

Over 220,000 entries representing some 56,000 Library of Congress subject headings. Covers all disciplines of science and technology, e.g., engineering, agriculture, and domestic arts. Also contains at least 5000 titles published before 1876. Has many applications in libraries, information centers, and other organizations concerned with scientific and technological literature. Subject index contains main listing of entries. Each entry gives cataloging as prepared by the Library of Congress. Author/title indexes.

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry.

Author: Hassan Akbar-Zadeh

Publisher: Elsevier

ISBN: 0080461700

Category: Mathematics

Page: 264

View: 799

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, projective and conformal vector fields on the unitary tangent fibre bundle. Key features - Theory of connections of vectors and directions on the unitary tangent fibre bundle. - Complete list of Bianchi identities for a regular conection of directions. - Geometry of generalized Einstein manifolds. - Classification of Finslerian manifolds. - Affine, isometric, conformal and projective vector fields on the unitary tangent fibre bundle. Theory of connections of vectors and directions on the unitary tangent fibre bundle. Complete list of Bianchi identities for a regular conection of directions. Geometry of generalized Einstein manifolds. Classification of Finslerian manifolds. Affine, isometric, conformal and projective vector fields on the unitary tangent fibre bundle.