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Connections, sprays, and Finsler str...

Szilasi, József,

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Connections, sprays, and Finsler structures /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Connections, sprays, and Finsler structures // József Szilasi, Rezső L Lovas, Dávid Cs Kertész, University of Debrecen, Hungary.
Author:	Szilasi, József,
other author:	Lovas, Rezső L.,
Published:	New Jersey :World Scientific, : [2014],
Description:	xxi, 709 pages :illustrations ;24 cm
[NT 15003449]:	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.
Subject:	Geometry, Differential. -
Online resource:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129169&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Online resource:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129169&line_number=0002&func_code=DB_RECORDS&service_type=MEDIAKlappentext
ISBN:	9789814440097

Connections, sprays, and Finsler structures /
Szilasi, József,

Connections, sprays, and Finsler structures /József Szilasi, Rezső L Lovas, Dávid Cs Kertész, University of Debrecen, Hungary. - New Jersey :World Scientific,[2014] - xxi, 709 pages :illustrations ;24 cm

Includes bibliographical references (pages 681-685) and indexes.

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.

This book provides a comprehensive introduction to Finsler geometry in the language of present-day 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 self-contained 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 index-free methods, they also apply the techniques of traditional tensor calculus. Most proofs are elaborated in detail, which makes the book suitable for self-study. 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.--

ISBN: 9789814440097

LCCN: 2012361281Subjects--Topical Terms:

523835
Geometry, Differential.

LC Class. No.: QA641 / .S95 2014

Dewey Class. No.: 516.36

Connections, sprays, and Finsler structures /
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100 1 $a Szilasi, József, $e author. $3 3814914
245 1 0 $a Connections, sprays, and Finsler structures / $c József Szilasi, Rezső L Lovas, Dávid Cs Kertész, University of Debrecen, Hungary.
260 # $a New Jersey : $b World Scientific, $c [2014]
300 $a xxi, 709 pages : $b illustrations ; $c 24 cm
504 $a Includes bibliographical references (pages 681-685) and indexes.
505 0 # $a 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.
520 3 $a This book provides a comprehensive introduction to Finsler geometry in the language of present-day 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 self-contained 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 index-free methods, they also apply the techniques of traditional tensor calculus. Most proofs are elaborated in detail, which makes the book suitable for self-study. 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.-- $c Source other than the Library of Congress.
650 # 0 $a Geometry, Differential. $3 523835
700 1 # $a Lovas, Rezső L., $e author. $3 3814915
700 1 # $a Kertész, Dávid Cs, $e author. $3 3814916
856 4 1 $3 Table of contents $u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129169&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
856 4 # $u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129169&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA $z Klappentext