- Title Pages
- Dedication
- Foreword
- Acknowledgments
- Part I Fundamental Concepts
- 0 Introduction
- 1 Parallelizable Manifolds
- 2 The Nonlinear Curvature
- 3 Local Lie Groups
- 4 The Centralizer
- 5 <i><span xml:lang="ell">ε</span></i>-Invariance
- 6 The Linear Curvature
- 7 The Structure Object
- Part II Some Consequences
- 8 The Nonlinear Spencer Sequence
- 9 Deformations
- 10 The de Rham Cohomology of an LLG
- 11 The Linear Spencer Sequence
- 12 The Secondary Characteristic Classes
- 13 The Homogeneous Flow
- 14 The Van Est Theorem
- 15 The Symmetry Group
- Part III How to Generalize?
- 16 Klein Geometries
- 17 The Universal Jet Groupoids
- 18 Embeddings of Klein Geometries into Universal Jet Groupoids
- 19 The Definition of a Prehomogeneous Geometry (PHG)
- 20 Curvature and Generalized PHGs
- Appendix Torsion-Free Connections
- References
- Index

# Curvature and Generalized PHGs

# Curvature and Generalized PHGs

- Chapter:
- (p.185) 20 Curvature and Generalized PHGs
- Source:
- An Alternative Approach to Lie Groups and Geometric Structures
- Author(s):
### Ercüment H. Ortaçgil

- Publisher:
- Oxford University Press

Even though it is quite clear at this stage what curvature means, its technical definition turns out to be problematic, since it needs a technical assumption. However, this assumption forces a projective structure to be flat, and it becomes necessary to modify the approach adopted so far.

*Keywords:*
prolongation of a PDE, formal integrability, tractor connection, Bloom connection, Bott connection

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- Title Pages
- Dedication
- Foreword
- Acknowledgments
- Part I Fundamental Concepts
- 0 Introduction
- 1 Parallelizable Manifolds
- 2 The Nonlinear Curvature
- 3 Local Lie Groups
- 4 The Centralizer
- 5 <i><span xml:lang="ell">ε</span></i>-Invariance
- 6 The Linear Curvature
- 7 The Structure Object
- Part II Some Consequences
- 8 The Nonlinear Spencer Sequence
- 9 Deformations
- 10 The de Rham Cohomology of an LLG
- 11 The Linear Spencer Sequence
- 12 The Secondary Characteristic Classes
- 13 The Homogeneous Flow
- 14 The Van Est Theorem
- 15 The Symmetry Group
- Part III How to Generalize?
- 16 Klein Geometries
- 17 The Universal Jet Groupoids
- 18 Embeddings of Klein Geometries into Universal Jet Groupoids
- 19 The Definition of a Prehomogeneous Geometry (PHG)
- 20 Curvature and Generalized PHGs
- Appendix Torsion-Free Connections
- References
- Index