Finsler几何：从Randers空间进入（英文版）

Finsler几何：从Randers空间进入（英文版）

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作者: 科学出版社编

出版社: 科学出版社

出版时间: 2012-01

版次: 1

ISBN: 9787030317650

定价: 68.00

装帧: 精装

开本: 16开

纸张: 胶版纸

页数: 150页

正文语种: 英语

分类: 自然科学

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This book exclusively deals with a special class of Finsler metricsRandersmetrics．Which are defined as the sum of a Riemannian metric and a l一form．Randers metrics derive from the research on General Relativity Theory andhavebeen applied in many areas of the natural sciences．They can also be naturallydeduced as the solution of the Zermelo navigation problem．The book providesreaders not only with essential findings on Randers metrics but also the core ideasand methods which are useful in Finsler geometry．It will be of significant interestto researchers and practitioners working in Finsler geometry，even in differentialgeometry or related natural fields．

Xinyue Cheng is a Professor at the School of Mathematics and Statistics ofChongqing University of Technology，China．Zhongmin Shen is a Professor at the Department ofMathematical Sciences ofIndiana University Purdue University，TISA. Chapter1RandersSpaces

1.1RandersNorms

1.2DistortionandVolumeForm

1.3CaftanTorsion

1.4Duality

Bibliography

Chapter2RandersMetricsandGeodesics

2.1RandersMetrics

2.2Zermelo'sNavigationProblem

2.3Geodesics

2.4RandersMetricsofBerwaldType

Bibliography

Chapter3RandersMetricsofIsotropicS-Curvature

3.1S-Curvature

3.2IsotropicS-CurvatureinTermsofaand/3

3.3IsotropicS-CurvatureinTermsofhandW

3.4ExamplesofIsotropicS-Curvature

3.5RandersMetricswithSecondaryIsotropicS-Curvature

Bibliography

Chapter4RiemannCurvatureandRicciCurvature

4.1Definitions

4.2RiemannCurvatureofRandersMetrics

4.3RandersMetricsofScalarFlagCurvature

Bibliography

Chapter5ProjectiveGeometryofRandersSpaces

5.1ProjectiveQuantities

5.2Douglas-RandersMetrics

5.3Weyl-RandersMetrics

5.4GeneralizedDouglasWeylRandersMetrics

Bibliography

Chapter6RandersMetricswithSpecialRiemannCurvatureProperties

6.1Ricci-QuadraticRandersMetrics

6.2RandersMetricsofR-QuadraticCurvature

6.3RandersMetricsofW-QuadraticCurvature

6.4RandersMetricsofSectionalFlagCurvature

Bibliography

Chapter7RandersMetricsofWeaklyIsotroplcFlagCurvature

7.1WeakEinsteinRandersMetrics

7.2RandersMetricsofWeaklyIsotropicFlagCurvature

7.3SolutionsviaNavigation

7.4WeakEinsteinRandersMetricsviaNavigationData

Bibliography

Chapter8ProjectivelyFlatRandersMetrics

8.1ProjectivelyFlatRandersMetricsofConstantFlagCurvature

8.2ProjectivelyFlatRandersMetricsofWeaklyIsotropicFlagCurvature

8.3ProjeetivelyFlatRandersMetricsonS

Bibliography

Chapter9ConformalGeometryofRandersMetrics

9.1ConformallyInvariantSpray

9.2ConformallyFlatRandersMetrics

9.3ConformallyBerwaldianRandersMetrics

Bibliography

Chapter10DuallyFlatRandersMetrics

10.1DuallyFlatFinslerMetrics

10.2DuallyFlatRandersMetrics

10.3DuallyFlatRandersMetricswithIsotropicS-Curvature

Bibliography

Index
内容简介:
This book exclusively deals with a special class of Finsler metricsRandersmetrics．Which are defined as the sum of a Riemannian metric and a l一form．Randers metrics derive from the research on General Relativity Theory andhavebeen applied in many areas of the natural sciences．They can also be naturallydeduced as the solution of the Zermelo navigation problem．The book providesreaders not only with essential findings on Randers metrics but also the core ideasand methods which are useful in Finsler geometry．It will be of significant interestto researchers and practitioners working in Finsler geometry，even in differentialgeometry or related natural fields．

Xinyue Cheng is a Professor at the School of Mathematics and Statistics ofChongqing University of Technology，China．Zhongmin Shen is a Professor at the Department ofMathematical Sciences ofIndiana University Purdue University，TISA.
目录:
Chapter1RandersSpaces

1.1RandersNorms

1.2DistortionandVolumeForm

1.3CaftanTorsion

1.4Duality

Bibliography

Chapter2RandersMetricsandGeodesics

2.1RandersMetrics

2.2Zermelo'sNavigationProblem

2.3Geodesics

2.4RandersMetricsofBerwaldType

Bibliography

Chapter3RandersMetricsofIsotropicS-Curvature

3.1S-Curvature

3.2IsotropicS-CurvatureinTermsofaand/3

3.3IsotropicS-CurvatureinTermsofhandW

3.4ExamplesofIsotropicS-Curvature

3.5RandersMetricswithSecondaryIsotropicS-Curvature

Bibliography

Chapter4RiemannCurvatureandRicciCurvature

4.1Definitions

4.2RiemannCurvatureofRandersMetrics

4.3RandersMetricsofScalarFlagCurvature

Bibliography

Chapter5ProjectiveGeometryofRandersSpaces

5.1ProjectiveQuantities

5.2Douglas-RandersMetrics

5.3Weyl-RandersMetrics

5.4GeneralizedDouglasWeylRandersMetrics

Bibliography

Chapter6RandersMetricswithSpecialRiemannCurvatureProperties

6.1Ricci-QuadraticRandersMetrics

6.2RandersMetricsofR-QuadraticCurvature

6.3RandersMetricsofW-QuadraticCurvature

6.4RandersMetricsofSectionalFlagCurvature

Bibliography

Chapter7RandersMetricsofWeaklyIsotroplcFlagCurvature

7.1WeakEinsteinRandersMetrics

7.2RandersMetricsofWeaklyIsotropicFlagCurvature

7.3SolutionsviaNavigation

7.4WeakEinsteinRandersMetricsviaNavigationData

Bibliography

Chapter8ProjectivelyFlatRandersMetrics

8.1ProjectivelyFlatRandersMetricsofConstantFlagCurvature

8.2ProjectivelyFlatRandersMetricsofWeaklyIsotropicFlagCurvature

8.3ProjeetivelyFlatRandersMetricsonS

Bibliography

Chapter9ConformalGeometryofRandersMetrics

9.1ConformallyInvariantSpray

9.2ConformallyFlatRandersMetrics

9.3ConformallyBerwaldianRandersMetrics

Bibliography

Chapter10DuallyFlatRandersMetrics

10.1DuallyFlatFinslerMetrics

10.2DuallyFlatRandersMetrics

10.3DuallyFlatRandersMetricswithIsotropicS-Curvature

Bibliography

Index

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