| Preface |
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1 | (17) |
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§ 1 Motions in a Riemannian space |
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1 | (5) |
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§ 2 Affine motions in a space with a linear connexion |
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6 | (3) |
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§ 3 Lie derivatives of scalars, vectors and tensors |
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9 | (6) |
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§ 4 The Lie derivative of a linear connexion |
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15 | (3) |
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Chapter II Lie Derivatives Of General Geometric Objects |
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18 | (12) |
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18 | (1) |
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§ 2 The Lie derivative of a geometric object |
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19 | (3) |
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§ 3 Miscellaneous examples of Lie derivatives |
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22 | (2) |
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§ 4 Some general formulas |
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24 | (6) |
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Chapter III Groups Of Transformations Leaving A Geometric Object Invariant |
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30 | (18) |
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§ 1 Projective and conformal motions |
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30 | (2) |
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§ 2 Invariance group of a geometric object |
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32 | (4) |
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§ 3 A group as invariance group of a geometric object |
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36 | (6) |
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§ 4 Generalizations of the preceding theorems |
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42 | (3) |
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45 | (3) |
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Chapter IV Groups Of Motions In Vn |
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48 | (37) |
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48 | (2) |
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§ 2 Groups of translations |
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50 | (1) |
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§ 3 Motions and affine motions |
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51 | (1) |
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§ 4 Some theorems on protectively or conformally related spaces |
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52 | (2) |
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§ 5 A theorem of Knebelman |
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54 | (2) |
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§ 6 Integrability conditions of Killing's equation |
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56 | (1) |
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§ 7 A group as group of motions |
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57 | (3) |
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60 | (3) |
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§ 9 Two theorems of Egorov |
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63 | (4) |
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§ 10 Vn's admitting a group Gr of motions of order r = 1/2n(n - 1) + 1 |
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67 | (8) |
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75 | (5) |
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80 | (5) |
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Chapter V Groups Of Affine Motions |
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85 | (45) |
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§ 1 Groups of affine motions |
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85 | (1) |
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§ 2 Groups of affine motions in a space with absolute parallelism |
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86 | (3) |
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§ 3 Infinitesimal transformations which carry affine conics into affine conics |
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89 | (2) |
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§ 4 Some theorems on affine and projective motions |
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91 | (2) |
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§ 5 Integrability conditions of v Γxμλ = 0 |
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93 | (2) |
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§ 6 An Ln with absolute parallelism which admits a simply transitive group of particular affine motions |
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95 | (3) |
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§ 7 Semi-simple group space |
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98 | (3) |
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§ 8 A group as group of affine motions |
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101 | (4) |
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§ 9 Groups of affine motions in an Ln or an An |
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105 | (6) |
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§ 10 Ln's admitting an n2-parameter complete group of motions |
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111 | (2) |
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§ 11 An's which admit a group of affine motions leaving invariant a symmetric covariant tensor of valence 2 |
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113 | (1) |
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§ 12 An's which admit a group of affine motions leaving invariant an alternating covariant tensor of valence 2 |
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114 | (4) |
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§ 13 Groups of affine motions in an An of order greater than n2 - n + 5 |
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118 | (12) |
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Chapter VI Groups Of Projective Motions |
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130 | (27) |
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§ 1 Groups of projective motions |
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130 | (1) |
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§ 2 Transformations carrying projective conics into projective conics |
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131 | (2) |
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§ 3 Integrability conditions of vΓxμλ = 2(μAxλ) |
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133 | (2) |
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§ 4 A group as group of projective motions |
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135 | (3) |
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§ 5 The maximum order of a group of projective motions in an An with non vanishing projective curvature |
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138 | (11) |
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§ 6 An An admitting a complete group of affine motions of order greater than n2 - n + 1 |
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149 | (6) |
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§ 7 An Ln admitting an n2-parameter group of affine motions |
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155 | (2) |
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Chapter VII Groups Of Conformal Motions |
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157 | (20) |
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§ 1 Groups of conformal motions |
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157 | (1) |
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§ 2 Transformations carrying conformal circles into conformal circles |
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158 | (2) |
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§ 3 Integrability conditions of vgμλ = 2φgμλ |
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160 | (4) |
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§ 4 A group as group of conformal motions |
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164 | (2) |
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166 | (4) |
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§ 6 Homothetic motions in conformally related spaces |
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170 | (1) |
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§ 7 Subgroups of homothetic motions contained in a group of conformal motions or in a group of affine motions |
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171 | (2) |
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§ 8 Integrability conditions of vgμλ = 2cgμλ |
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173 | (1) |
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§ 9 A group as group of homothetic motions |
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174 | (3) |
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Chapter VIII Groups Of Transformations In Generalized Spaces |
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177 | (37) |
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177 | (2) |
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§ 2 Lie derivative of the fundamental tensor |
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179 | (1) |
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§ 3 Motions in a Finsler space |
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180 | (2) |
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§ 4 Finsler spaces with completely integrable equations of Killing |
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182 | (3) |
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§ 5 General affine spaces of geodesies |
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185 | (3) |
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§ 6 Lie derivatives in a general affine space of geodesies |
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188 | (2) |
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§ 7 Affine motions in a general affine space of geodesies |
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190 | (1) |
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§ 8 Integrability conditions of the equations vΓxμλ= 0 |
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190 | (4) |
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§ 9 General projective spaces of geodesies |
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194 | (5) |
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§ 10 Projective motions in a general projective space of geodesies |
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199 | (2) |
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§ 11 Integrability conditions of vΠxμλ = μAxμ + λAxμ |
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201 | (6) |
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§ 12 Affine spaces of k-spreads |
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207 | (4) |
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§ 13 Projective spaces of k-spreads |
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211 | (3) |
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Chapter IX Lie Derivatives In A Compact Orientable Riemannian Space |
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214 | (11) |
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214 | (1) |
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215 | (2) |
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§ 3 Lie derivative of a harmonic tensor |
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217 | (1) |
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§ 4 Motions in a compact orientable Vn |
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218 | (3) |
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§ 5 Affine motions in a compact orientable Vn |
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221 | (1) |
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222 | (1) |
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§ 7 Isotropy groups and holonomy groups |
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223 | (2) |
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Chapter X Lie Derivatives In An Almost Complex Space |
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225 | (19) |
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§ 1 Almost complex spaces |
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225 | (3) |
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§ 2 Linear connexions in an almost complex space |
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228 | (2) |
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§ 3 Almost complex metric spaces |
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230 | (3) |
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§ 4 The curvature in a pseudo-Kahlerian space |
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233 | (2) |
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§ 5 Pseudo-analytic vectors |
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235 | (3) |
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§ 6 Pseudo-Kahlerian spaces of constant holomorphic curvature |
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238 | (6) |
| Bibliography |
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244 | (19) |
| Appendix |
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263 | (25) |
| Bibliography |
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288 | (7) |
| Author Index |
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295 | (3) |
| Subject Index |
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298 | |
