Buy Geometry and Algebra of Multidimensional Three-Webs
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Home > Mathematics and Science Textbooks > Mathematics > Geometry > Differential and Riemannian geometry > Geometry and Algebra of Multidimensional Three-Webs: (82 Mathematics and its Applications)
Geometry and Algebra of Multidimensional Three-Webs: (82 Mathematics and its Applications)

Geometry and Algebra of Multidimensional Three-Webs: (82 Mathematics and its Applications)


     0     
5
4
3
2
1



Available


X
About the Book

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. The volume contains eight chapters dealing with h-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". This volume should be of particular interest to graduate students and researchers working in the areas of differential and algebraic geometry and algebra.

Table of Contents:
1 Three-Webs and Geometric Structures Associated with Them.- 1.1 G-Structures, Fibrations and Foliations.- 1.2 Three-Webs on Smooth Manifolds.- 1.3 Geometry of the Tangent Space of a Multidimensional Three-Web.- 1.4 Structure Equations of a Multidimensional Three-Web.- 1.5 Parallelizable and Group Three-Webs.- 1.6 Computation of the Torsion and Curvature Tensors of a Three-Web.- 1.7 The Canonical Chern Connection on a Three-Web.- 1.8 Other Connections Associated with a Three-Web.- 1.9 Subwebs of Multidimensional Three-Webs.- Problems.- Notes.- 2 Algebraic Structures Associated with Three-Webs.- 2.1 Quasigroups and Loops.- 2.2 Configurations in Abstract Three-Webs.- 2.3 Identities in Coordinate Loops and Closure Conditions.- 2.4 Local Differentiable Loops and Their Tangent Algebras.- 2.5 Tangent Algebras of a Multidimensional Three-Web.- 2.6 Canonical Coordinates in a Local Analytic Loop.- 2.7 Algebraic Properties of the Chern Connection.- Problems.- Notes.- 3 Transversally Geodesic and Isoclinic Three-Webs.- 3.1 Transversally Geodesic and Hexagonal Three-Webs.- 3.2 Isoclinic Three-Webs.- 3.3 Grassmann Three-Webs.- 3.4 An Almost Grassmann Structure Associated with a Three-Web. Problems of Grassmannization and Algebraization.- 3.5 Isoclinicly Geodesic Three-Webs. Three-Webs over Algebra.- Problems.- Notes.- 4 The Bol Three-Webs and the Moufang Three-Webs.- 4.1 The Bol Three-Webs.- 4.2 The Isoclinic Bol Three-Webs.- 4.3 The Six-Dimensional Bol Three-Webs.- 4.4 The Moufang Three-Webs.- 4.5 The Moufang Three-Web of Minimal Dimension.- Problems.- Notes.- 5 Closed G-Structures Associated with Three-Webs.- 5.1 Closed G-Structures on a Smooth Manifold.- 5.2 Closed G-Structures Defined by Multidimensional Three-Webs.- 5.3 Four-dimensional Hexagonal Three-Webs.- 5.4 The Closure ofThe G-Structure Defined by a Multidimensional Hexagonal Three-Web.- 5.5 Three-Webs and Identities in Loops.- Problems.- Notes.- 6 Automorphisms of Three-Webs.- 6.1 The Autotopies of Quasigroups and Three-Webs.- 6.2 Infinitesimal Automorphisms of Three-Webs.- 6.3 Regular Infinitesimal Automorphisms of Three-Webs.- 6.4 G-Webs.- Problems.- Notes.- 7 Geometry of the Fourth Order Differential Neighborhood of a Multidimensional Three-Web.- 7.1 Computation of Covariant Derivatives of the Curvature Tensor of a Three-Web.- 7.2 Internal Mappings in Coordinate Loops of a Three-Web.- 7.3 An Algebraic Characterization of the Tangent W4-Algebra of a Three-Web.- 7.4 Classification of Three-Webs in the Fourth Order Differential Neighborhood.- 7.5 Three-Webs with Elastic Coordinate Loop.- Problems.- Notes.- 8 d-Webs of Codimension r.- 8.1 (n + 1)-Webs on a Manifold of Dimension nr.- 8.2 (n + 1)-Webs on a Grassmann Manifold.- 8.3 (n + 1)-Webs and Almost Grassmann Structures.- 8.4 Transversally Geodesic and Isoclinic (n + 1)-Webs.- 8.5 d-Webs on a Manifold of Dimension nr.- 8.6 The Algebraization Problem for Multidimensional d-Webs.- 8.7 The Rank Problem for d-Webs.- Problems.- Notes.- Appendix A.- Symbols Frequently Used.

Review :
'The book is warmly recommended to everyone doing research in the related fields.' Deutschen Mathematiker-Vereinigung 97:21 1993


Best Sellers


Product Details
  • ISBN-13: 9780792316848
  • Publisher: Kluwer Academic Publishers
  • Publisher Imprint: Kluwer Academic Publishers
  • Height: 235 mm
  • No of Pages: 358
  • Series Title: 82 Mathematics and its Applications
  • ISBN-10: 0792316843
  • Publisher Date: 31 Mar 1992
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Width: 155 mm


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Geometry and Algebra of Multidimensional Three-Webs: (82 Mathematics and its Applications)
Kluwer Academic Publishers -
Geometry and Algebra of Multidimensional Three-Webs: (82 Mathematics and its Applications)
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Geometry and Algebra of Multidimensional Three-Webs: (82 Mathematics and its Applications)

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!