This book focuses on the elementary but essential problems in Riemann-Finsler Geometry, which include a repertoire of rigidity and comparison theorems, and an array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. "This book offers the most modern treatment of the topic …" EMS Newsletter.
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Editorial Reviews
Review
"Das Buch ist sehr gut strukturiert und stellt die doch umfangreiche Materie klar dar. Es wendet sich an Studenten höherer Semester und erlaubt einen guten Einstieg in das weite Gebiet der Finsler-Geometrie. Für alle Interessierten bietet das Werk einen klaren Zugang, der auch die geschichtliche Entwicklung von der Euklidischen über die Riemannsche zur Finslerschen Geometrie deutlich macht." Internationale Mathematische Nachrichten, Nr. 187, August 2001
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2 of 3 people found the following review helpful:
4.0 out of 5 stars
Mainly for experts in Finsler geometry,
By Dr. Oliver Strebel (Berlin, Deutschland) - See all my reviews
This review is from: An Introduction to Riemann-Finsler Geometry (Graduate Texts in Mathematics) (Hardcover)
The authors claim to turn the subject of Finsler geometry with this book
into a more teachable one and to have a candid style of writing. This is definitly true for the first 50 pages, where the concepts of Finsler geometry are very well explained and the exercises are manageable and perfectly interrelated with the text. Then the Chern connection and the curvature tensor of Finsler geometry drop out of the heaven without any explanation of the ideas leading to these constructions. So one has to derive them alone. In doing so older texts on Finsler geometry like the Grundlehren text of Rund are more helpful than this volume. But the book was apparently prepared with great care. The layout must be called beautyful and it really facilitates reading this book. Many references to the literature and classical papers of the subject are included. So beginners, which want to get a first aquaintance in Finsler geometry, find at least some help.
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Inside This Book
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First Sentence:
Finsler geometry has its genesis in integrals of the form. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
flag curvature, geodesic spray coefficients, geodesic expx, geodesic expp, indicatrix bundle, divergence lemma, first conjugate point, conjugate loci, exponential map expp, constant speed geodesic, interchange formula, unit speed geodesic, metric discs, minimizes arc length, nonlinear connection, fundamental tensor, strong convexity, smooth geodesic, metric ball, geodesic completeness, canonical lift, geometrical setup, torsion freeness, geodesic rays, variation vector field Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercises Exercise, Differential Geometry, Elegant Theorem, Generalized Gauss-Bonnet Theorem, Effect of Curvature, Variations of Arc Length, Covering Homotopy, Kaiseisha Press, Kluwer Academic Publishers, Academic Press, Disc That Is Only Forward Complete, American Elsevier, Comparison Theorems, Inverse Function, North Holland, Explicit Examples of Finsler Manifolds, Kyoto Daigaku, Kyoto Univ, Non-Riemannian Projectively Flat, Short Geodesics Are Minimizing, Two Basic Properties of Minkowski Norms, Useful Basis, Coordinate Bases Versus Special Orthonormal Bases, Exercise Exercise, Kagoshima Univ New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Finsler geometry has its genesis in integrals of the form. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
flag curvature, geodesic spray coefficients, geodesic expx, geodesic expp, indicatrix bundle, divergence lemma, first conjugate point, conjugate loci, exponential map expp, constant speed geodesic, interchange formula, unit speed geodesic, metric discs, minimizes arc length, nonlinear connection, fundamental tensor, strong convexity, smooth geodesic, metric ball, geodesic completeness, canonical lift, geometrical setup, torsion freeness, geodesic rays, variation vector field Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercises Exercise, Differential Geometry, Elegant Theorem, Generalized Gauss-Bonnet Theorem, Effect of Curvature, Variations of Arc Length, Covering Homotopy, Kaiseisha Press, Kluwer Academic Publishers, Academic Press, Disc That Is Only Forward Complete, American Elsevier, Comparison Theorems, Inverse Function, North Holland, Explicit Examples of Finsler Manifolds, Kyoto Daigaku, Kyoto Univ, Non-Riemannian Projectively Flat, Short Geodesics Are Minimizing, Two Basic Properties of Minkowski Norms, Useful Basis, Coordinate Bases Versus Special Orthonormal Bases, Exercise Exercise, Kagoshima Univ New!
Books on Related Topics | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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69
books
cite this book:
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- Differential Geometry (Proceedings of Symposia in Pure Mathematics, vol. 27, pt. 2) by Shiing-Shen Chern on 11 pages
- The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology (Fundamental Theories of Physics) by P.L. Antonelli on 7 pages
- Differential Geometry: Manifolds, Curves, and Surfaces (Graduate Texts in Mathematics) by Marcel Berger on 4 pages
- Global Differential Geometry (Studies in Mathematics, Vol 27) by S. S. Chern on page 198, page 224, and Back Matter
- Foundations of Differentiable Manifolds and Lie Groups (Graduate Texts in Mathematics) (v. 94) by Frank W. Warner on page 382, Back Matter (1), and Back Matter (2)
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- Finsler and Lagrange Geometries (NATO Science) by Mihai Anastasiei on 6 pages
- Lectures on Differential Geometry (Series on University Mathematics) by Shiing-Shen Chern in Front Matter, and Back Matter
- An Introduction to Markov Processes (Graduate Texts in Mathematics) by Daniel W. Stroock in Back Matter
- 1,001 Low-Fat Vegetarian Recipes: Delicious, Easy-to-Make, Healthy Meals for Everyone by Sue Spitler on page 197
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Back Matter
See all 69 books citing this book
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