Description

Book Synopsis
Focuses on several successful classification problems. Namely, fix a geometry in the sense of Klein and a topological manifold. Then the different ways of locally putting the geometry on the manifold lead to a moduli space'.

Table of Contents
  • Part 1. Affine and projective geometry: Affine geometry
  • Projective geometry
  • Duality and non-Euclidean geometry
  • Convexity
  • 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
  • Bibliography
  • Index

Geometric Structures on Manifolds

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    A Paperback by William M. Goldman

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      Publisher: MP-AMM American Mathematical
      Publication Date: 1/30/2023 12:00:00 AM
      ISBN13: 9781470471989, 978-1470471989
      ISBN10: 1470471981
      Also in:
      Topology

      Description

      Book Synopsis
      Focuses on several successful classification problems. Namely, fix a geometry in the sense of Klein and a topological manifold. Then the different ways of locally putting the geometry on the manifold lead to a moduli space'.

      Table of Contents
      • Part 1. Affine and projective geometry: Affine geometry
      • Projective geometry
      • Duality and non-Euclidean geometry
      • Convexity
      • 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
      • Bibliography
      • Index

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