| 中文摘要 | 第1-7页 |
| Abstract | 第7-11页 |
| Chapter 1 Introduction | 第11-21页 |
| ·Background | 第11-14页 |
| ·A Brief Survey of Homogeneous Einstein Manifolds | 第14-19页 |
| ·Our Work | 第19-21页 |
| Chapter 2 Preliminaries | 第21-39页 |
| ·Notion and Notations | 第21-26页 |
| ·Pseudo-Riemannian manifolds and pseudo-Einstein manifolds | 第21-22页 |
| ·Left-invariant metrics on Lie groups | 第22-24页 |
| ·Real forms and semisimple Lie algebras | 第24-26页 |
| ·Classification Theory of Real Semisimple Lie Algebras | 第26-39页 |
| ·Theorem of Gantmacher and regular characteristic subalgebras | 第26-28页 |
| ·Classification of real simple Lie algebras | 第28-35页 |
| ·Involutions of canonical real simple Lie algebras | 第35-39页 |
| Chapter 3 RicciCurvatureFormulaandExamplesofpseudo-Einstein metrics | 第39-53页 |
| ·AFormulaofRicciCurvaturesAssociatedwithPseudo-Riemannian Metrics | 第39-42页 |
| ·Examplesofpseudo-Einsteinmetricsonlow-dimensionalLiegroups | 第42-47页 |
| ·Some observations | 第42-44页 |
| ·Left-invariant pseudo-Einstein metrics on 3-dimensional unimodular Lie groups | 第44-47页 |
| ·Left-InvariantPseudo-EinsteinMetricsonLow-DimensionalCom-pact Lie Groups | 第47-53页 |
| ·Simplify the Ricci curvature formula for compact Lie Groups | 第47-48页 |
| ·Pseudo-Einstein metrics on low-dimensional compact Lie groups | 第48-53页 |
| Chapter 4 Left-InvariantPseudo-EinsteinMetricsonNoncompactSemisim-ple Lie Groups | 第53-83页 |
| ·Ricci Curvature Relationship between Compact and Noncompact Semisimple Lie Groups | 第53-57页 |
| ·An observation | 第53-54页 |
| ·Ricci curvatures on compact Lie groups with involutions | 第54-56页 |
| ·Ricci curvatures on the noncompact semisimple Lie groups constructed from the compact Lie groups above | 第56-57页 |
| ·ConstructionofPseudo-EinsteinMetricsonNoncompactSemisim- ple Lie Groups | 第57-81页 |
| ·Correspondence of pseudo-Einstein metrics on a couple of Lie groups | 第57-58页 |
| ·Pseudo-Einstein metrics on noncompact semisimple Lie groups of type A | 第58-70页 |
| ·Pseudo-Einstein metrics on noncompact semisimple Lie groups of type BD60 | 第70-81页 |
| ·Further Discussions | 第81-83页 |
| ·Additional left-invariant pseudo-Einstein metrics | 第81页 |
| ·Difficulties to classify pseudo-Einstein metrics on a noncompact Lie group | 第81-83页 |
| References | 第83-87页 |
| 致谢 | 第87-89页 |
| 个人简历 | 第89页 |
| 附 学术论文成果 | 第89-90页 |
