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Geometric Structures on Manifolds
About this Title
William M. Goldman, University of Maryland, College Park, MD
Publication: Graduate Studies in Mathematics
Publication Year:
2022; Volume 227
ISBNs: 978-1-4704-7103-3 (print); 978-1-4704-7197-2 (online)
DOI: https://doi.org/10.1090/gsm/227
Table of Contents
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Front/Back Matter
Part 1. Affine and projective geometry
Part 2. Geometric manifolds
- Locally homogeneous geometric structures
- Examples of geometric structures
- Classification
- Completeness
Part 3. Affine and projective structures
- Affine structures on surfaces and the Euler characteristic
- Affine Lie groups
- Parallel volume and completeness
- Hyperbolicity
- Projective structures on surfaces
- Complex-projective structures
- Geometric structures on 3-manifolds
Appendices
- Appendix A. Transformation groups
- Appendix B. Affine connections
- Appendix C. Representations of nilpotent groups
- Appendix D. 4-dimensional filiform nilpotent Lie algebras
- Appendix E. Semicontinuous functions
- Appendix F. $\mathsf {SL}(2,\mathbb {C})$ and $O(3,1)$
- Appendix G. Lagrangian foliations of symplectic manifolds
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