Connections, sprays and Finsler structures
 Author/Creator
 Szilasi, József.
 Language
 English.
 Publication
 Singapore ; Hackensack, NJ : World Scientific, [2014].
 Physical description
 xxi, 709 pages : ill. ; 24 cm
Access
Available online

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QA641 .S98 2014

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QA641 .S98 2014
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Contributors
 Contributor
 Lovas, Rezső L.
 Kertész, Dávid Cs.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 681685) and indexes.
 Contents

 1. Modules, algebras and derivations
 2. Manifolds and bundles
 3. Vector fields, tensors and integration
 4. Structures on tangent bundles
 5. Sprays and Lagrangian's
 6. Covariant derivatives
 7. Theory of Ehresmann connections
 8. Geometry of spray manifolds
 9. Finsler norms and Finsler functions
 Appendices.
 Summary
 This book provides a comprehensive introduction to Finsler geometry in the language of presentday mathematics. Through Finsler geometry, it also introduces the reader to other structures and techniques of differential geometry.Prerequisites for reading the book are minimal: undergraduate linear algebra (over the reals) and analysis. The necessary concepts and tools of advanced linear algebra (over modules), point set topology, multivariable calculus and the rudiments of the theory of differential equations are integrated in the text. Basic manifold and bundle theories are treated concisely, carefully and (apart from proofs) in a selfcontained manner.The backbone of the book is the detailed and original exposition of tangent bundle geometry, Ehresmann connections and sprays. It turns out that these structures are important not only in their own right and in the foundation of Finsler geometry, but they can be also regarded as the cornerstones of the huge edifice of Differential Geometry.The authors emphasize the conceptual aspects, but carefully elaborate calculative aspects as well (tensor derivations, graded derivations and covariant derivatives). Although they give preference to indexfree methods, they also apply the techniques of traditional tensor calculus.Most proofs are elaborated in detail, which makes the book suitable for selfstudy. Nevertheless, the authors provide for more advanced readers as well by supplying them with adequate material, and the book may also serve as a reference.
Subjects
 Subject
 Geometry, Differential.
Bibliographic information
 Publication date
 2014
 Responsibility
 József Szilasi, Rezső L Lovas, Dávid Cs Kertész.
 ISBN
 9814440094
 9789814440097