| Preface |
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vii | |
| 1. Riemannian Submersions |
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1 | (32) |
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1.1 Riemannian Submersions |
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2 | (2) |
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4 | (4) |
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1.3 Fundamental Tensors and Fundamental Equations |
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8 | (9) |
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17 | (8) |
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1.5 Geodesics and O'Neill Theorem |
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25 | (3) |
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28 | (5) |
| 2. Submersions with Totally Geodesic Fibres |
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33 | (26) |
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2.1 Riemannian Submersions with Complete Total Space |
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34 | (4) |
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2.2 Submersions with Totally Geodesic Fibres |
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38 | (6) |
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2.3 Riemannian Submersions from the Spheres |
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44 | (5) |
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2.4 The Uniqueness Theorem |
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49 | (5) |
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2.5 Submersions from the Complex Projective Spaces |
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54 | (5) |
| 3. Almost Hermitian Submersions |
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59 | (44) |
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3.1 Almost Hermitian Manifolds |
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60 | (4) |
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3.2 Almost Hermitian Submersions |
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64 | (7) |
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3.3 Holomorphic Distributions in Kähler Submersions |
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71 | (4) |
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75 | (6) |
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3.5 Locally Conformal Kähler Manifolds |
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81 | (7) |
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3.6 Locally Conformal Kähler Submersions |
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88 | (3) |
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3.7 Submersions from Generalized Hopf Manifolds |
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91 | (6) |
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3.8 Almost Complex Conformal Submersions |
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97 | (6) |
| 4. Riemannian Submersions and Contact Metric Manifolds |
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103 | (40) |
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4.1 Remarkable Classes of Contact Metric Manifolds |
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104 | (5) |
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4.2 Contact Riemannian Submersions |
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109 | (5) |
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4.3 Contact-complex Riemannian Submersions |
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114 | (2) |
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4.4 Complex-contact Riemannian Submersions |
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116 | (4) |
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120 | (2) |
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4.6 Riemannian Submersions Involving Quaternionic Kähler and 3-Sasakian Manifolds |
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122 | (7) |
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4.7 Regular f -structures and Riemannian Submersions |
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129 | (14) |
| 5. Einstein Spaces and Riemannian Submersions |
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143 | (52) |
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5.1 Einstein Metrics on the Total Space of a Riemannian Submersion |
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144 | (4) |
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5.2 The Canonical Variation of the Metric in the Total Space |
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148 | (5) |
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5.3 Homogeneous Einstein Spaces |
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153 | (9) |
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5.4 Einstein Metrics on Principal Bundles |
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162 | (13) |
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5.5 Einstein Weyl Structures on Principal Bundles |
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175 | (7) |
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5.6 Einstein Weyl Structures on Hermitian and Sasakian Manifolds |
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182 | (13) |
| 6. Riemannian Submersions and Submanifolds |
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195 | (20) |
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6.1 Submersions of CR-submanifolds |
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196 | (5) |
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6.2 Links Between Submanifolds of Sasakian and Kähler Manifolds |
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201 | (8) |
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6.3 Riemannian Submersions and Isometric Reflections with Respect to the Fibres |
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209 | (6) |
| 7. Semi-Riemannian Submersions |
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215 | (24) |
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7.1 Semi-Riemannian Manifolds |
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216 | (2) |
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7.2 Semi-Riemannian Submersions. Examples |
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218 | (3) |
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7.3 Lorentzian Submersions |
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221 | (2) |
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7.4 Submersions from Pseudo-hyperbolic Spaces |
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223 | (9) |
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7.5 Submersions with Totally Umbilical Fibres |
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232 | (4) |
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7.6 Semi-Riemannian Submersions with Minimal Fibres |
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236 | (3) |
| 8. Applications of Riemannian Submersions in Physics |
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239 | (18) |
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8.1 Gauge Fields, Instantons and Riemannian Submersions |
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239 | (4) |
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8.2 Einstein Equations and Kaluza-Klein Ansatz |
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243 | (3) |
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8.3 Generalized Nonlinear Sigma Model in Curved Space |
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246 | (4) |
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8.4 Horizontally Conformal Submersions and Gravity |
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250 | (1) |
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8.5 The Dirac Monopole and the Hopf Map |
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251 | (4) |
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8.6 Kaluza-Klein Monopole and Taub-NUT Instanton |
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255 | (2) |
| Bibliography |
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257 | (18) |
| Index |
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275 | |
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