Geometry and algebra of multidimensional three-webs

by Maks A. Akivis and Alexander M. Shelekhov ; translated from Russian by Vladislav V. Goldberg

This monograph, which is the first to be devoted to the geometry of multidimensional three-webs, presents the classical adn up-to-date 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. The volume contains eight chapters dealing with geometric and algebraic structures associated with three-webs, transversally geodesic and isoclinic three-webs, Bol and Moufang three-webs, closed G-structures, automorphisms of three-webs, the geometry of the fourth-order differential neighborhood of a multidimensional three-web, and d-webs of codimension r. The book concludes with some appendices and a comprehensive bibliography. This volume will be of particular interest to graduate students and researchers working in the areas of differential and algebraic geometry and algebra.

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  • Preface. 1. Three-Webs and Geometric Structures Associated with Them. 2. Algebraic Structures Associated with Three-Webs. 3. Transversally Geodesic and Isoclinic Three-Webs. 4. The Bol Three-Webs and the Moufang Three-Webs. 5. Closed G-Structures Associated with Three-Webs. 6. Automorphisms of Three-Webs. 7. Geometry of the Fourth Order Differential Neighborhood of a Multidimensional Three-Web. 8. d-Webs of Codimension r. Appendix A. Web Geometry and Mathematical Physics
  • E.V. Ferapontov. Bibliography. Symbols Frequently Used. Index.

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書名 Geometry and algebra of multidimensional three-webs
著作者等 Akivis, M. A.
Shelekhov, A. M
Goldberg V.V.
Shelekhov Alexander M.
Akivis M. A.
シリーズ名 Mathematics and its applications
出版元 Kluwer Academic Publishers
刊行年月 c1992
ページ数 xvii, 358 p.
大きさ 25 cm
ISBN 0792316843
NCID BA14338370
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言語 英語
原文言語 ロシア語
出版国 オランダ