Lifts of geometric objects to bundles 幾何学的対象のバンドルへの引き上げ
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著者
書誌事項
- タイトル
-
Lifts of geometric objects to bundles
- タイトル別名
-
幾何学的対象のバンドルへの引き上げ
- 著者名
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関沢, 正躬, 1944-
- 著者別名
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セキザワ, マサミ
- 学位授与大学
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東京都立大学
- 取得学位
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理学博士
- 学位授与番号
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乙第750号
- 学位授与年月日
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1990-12-20
注記・抄録
博士論文
目次
- Contents / p1 (0006.jp2)
- 1 LIFTS OF REDUCTIVE HOMOGENEOUS SPACES / p3 (0008.jp2)
- 1.1.Tangent Bundles / p4 (0009.jp2)
- 1.2.Tangent Groups / p6 (0011.jp2)
- 1.3.Tangent Bundles over Reductive Homogeneous Spaces / p11 (0016.jp2)
- 1.4.Tangent Bundles over Regular s-manifolds / p16 (0021.jp2)
- 1.5.Another Proof in a Special Case / p23 (0028.jp2)
- 2 RIEMANNIAN Σ-SPACES / p27 (0032.jp2)
- 2.1.Σ-structures and Regular s-structures / p27 (0032.jp2)
- 2.2.Regular s-structures of Maximal Type / p31 (0036.jp2)
- 2.3.3-dimensional Classification / p35 (0040.jp2)
- 3 LIFTS TO TANGENT BUNDLES / p41 (0046.jp2)
- 3.1.Natural Transformations and Differential Invariants / p42 (0047.jp2)
- 3.2.Classical lifts of vector fields / p45 (0050.jp2)
- 3.3.Natural Transformations of Vector Fields / p47 (0052.jp2)
- 3.4.Pointwise Natural Transformations of Vector Fields / p54 (0059.jp2)
- 3.5.Classical Lifts of Metrics / p56 (0061.jp2)
- 3.6.A Necessary Condition / p58 (0063.jp2)
- 3.7.Naturally Derived F-metrics / p63 (0068.jp2)
- 3.8.Natural Transformations of Metrics / p78 (0083.jp2)
- 4 LIFTS TO COTANGENT BUNDLES AND TO LINEAR FRAME BUNDLES / p81 (0086.jp2)
- 4.1.The Canonical 1-form and the Riemann Extension / p82 (0087.jp2)
- 4.2.Natural Transformations of Connections to Metrics on T*M / p84 (0089.jp2)
- 4.3.Classical Lifts of Metrics to Metric on LM / p89 (0094.jp2)
- 4.4.Natural Transformations of Metrics to Metrics on LM / p93 (0098.jp2)
- 4.5.Naturally Derived L-metrics / p97 (0102.jp2)
- 4.6.Classical Lifts of Connections to Metrics on LM / p101 (0106.jp2)
- 4.7.Natural Transformations of Connections to Metrics on LM / p102 (0107.jp2)
- 5 CURVATURES OF TANGENT BUNDLES WITH CHEEGER-GROMOLLMETRIC / p109 (0114.jp2)
- 5.1.The Cheeger-Gromoll Metric / p110 (0115.jp2)
- 5.2.The Levi-Civita Connection / p112 (0117.jp2)
- 5.3.The Riemannian Curvature / p114 (0119.jp2)
- 5.4.Sectional Curvatures / p116 (0121.jp2)
- 5.5.The Scalar Curvature / p118 (0123.jp2)