Lorentzian manifolds with special holonomy – Constructions and global properties
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Helga Baum
Abstract
We report on several new results concerning global properties of Lorentzian manifolds with special holonomy. The first states that compact Lorentzian manifolds with abelian holonomy are geodesically complete. The second describes a Bochnertype estimate for the first Betti number of Lorentzian manifolds with a parallel lightlike vector field V and nonnegative Ricci tensor along V⊥. In the third part, we discuss Cauchy problems that allow to construct Lorentzian manifolds with special holonomy using appropriate evolution equations for initial data on Riemannian manifolds.
Abstract
We report on several new results concerning global properties of Lorentzian manifolds with special holonomy. The first states that compact Lorentzian manifolds with abelian holonomy are geodesically complete. The second describes a Bochnertype estimate for the first Betti number of Lorentzian manifolds with a parallel lightlike vector field V and nonnegative Ricci tensor along V⊥. In the third part, we discuss Cauchy problems that allow to construct Lorentzian manifolds with special holonomy using appropriate evolution equations for initial data on Riemannian manifolds.
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Introduction VII
- Algebraic K-theory, assembly maps, controlled algebra, and trace methods 1
- Lorentzian manifolds with special holonomy – Constructions and global properties 51
- Contributions to the spectral geometry of locally homogeneous spaces 69
- On conformally covariant differential operators and spectral theory of the holographic Laplacian 90
- Moduli and deformations 116
- Vector bundles in algebraic geometry and mathematical physics 150
- Dyson–Schwinger equations: Fix-point equations for quantum fields 186
- Hidden structure in the form factors of N = 4 SYM 197
- On regulating the AdS superstring 221
- Constraints on CFT observables from the bootstrap program 245
- Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities 266
- Yangian symmetry inmaximally supersymmetric Yang-Mills theory 288
- Wave and Dirac equations on manifolds 324
- Geometric analysis on singular spaces 349
- Singularities and long-time behavior in nonlinear evolution equations and general relativity 417
- Index 491
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Introduction VII
- Algebraic K-theory, assembly maps, controlled algebra, and trace methods 1
- Lorentzian manifolds with special holonomy – Constructions and global properties 51
- Contributions to the spectral geometry of locally homogeneous spaces 69
- On conformally covariant differential operators and spectral theory of the holographic Laplacian 90
- Moduli and deformations 116
- Vector bundles in algebraic geometry and mathematical physics 150
- Dyson–Schwinger equations: Fix-point equations for quantum fields 186
- Hidden structure in the form factors of N = 4 SYM 197
- On regulating the AdS superstring 221
- Constraints on CFT observables from the bootstrap program 245
- Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities 266
- Yangian symmetry inmaximally supersymmetric Yang-Mills theory 288
- Wave and Dirac equations on manifolds 324
- Geometric analysis on singular spaces 349
- Singularities and long-time behavior in nonlinear evolution equations and general relativity 417
- Index 491
