The Dirac spectrum of Bieberbach manifolds

DOI10.1016/S0393-0440(00)00005-XzbMath0984.58017WikidataQ126981823 ScholiaQ126981823MaRDI QIDQ5931240

Frank Pfäffle

Publication date: 30 April 2002

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

spectrumDirac operatoreta invariantBieberbach manifoldsparallel spinors

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spin and Spin({}^c) geometry (53C27) Eta-invariants, Chern-Simons invariants (58J28)

Related Items (30)

GEOMETRY OF SPIN ANDSPIN^cSTRUCTURES IN THE M-THEORY PARTITION FUNCTION ⋮ A spinorial energy functional: critical points and gradient flow ⋮ Some conformally flat spin manifolds, Dirac operators and automorphic forms ⋮ Nothing is certain in string compactifications ⋮ Manifolds with small Dirac eigenvalues are nilmanifolds ⋮ Real spectral triples over noncommutative Bieberbach manifolds ⋮ Fractality in cosmic topology models with spectral action gravity ⋮ Dirac cohomology on manifolds with boundary and spectral lower bounds ⋮ Cusps and commensurability classes of hyperbolic 4-manifolds ⋮ Heterotic strings on \(\mathbb{T}^3/\mathbb{Z}_2\), Nikulin involutions and M-theory ⋮ CLASSIFICATION OF SPIN STRUCTURES ON FOUR‐DIMENSIONAL ALMOST‐FLAT MANIFOLDS ⋮ The Schrödinger semigroup on some flat and non flat manifolds ⋮ The spectrum of Schrödinger operators and Hodge Laplacians on conformally cusp manifolds ⋮ Supersymmetry, Ricci flat manifolds and the string landscape ⋮ The coupling of topology and inflation in noncommutative cosmology ⋮ Eta invariants for flat manifolds ⋮ Spectral asymmetry of the massless Dirac operator on a 3-torus ⋮ The spectral action and cosmic topology ⋮ A spectral estimate for the Dirac operator on Riemannian flows ⋮ Parallel spinors on flat manifolds ⋮ The eta invariant and equivariant bordism of flat manifolds with cyclic holonomy group of odd prime order ⋮ Stringy tachyonic instabilities of non-supersymmetric Ricci flat backgrounds ⋮ Boundaries of locally conformally flat manifolds in dimensions $4k$ ⋮ Spin structures on flat manifolds ⋮ Spin structures on flat manifolds ⋮ The spectrum of twisted Dirac operators on compact flat manifolds ⋮ Flat manifolds, harmonic spinors, and eta invariants ⋮ Geometric aspects of transversal Killing spinors on Riemannian flows ⋮ Dirac and Laplace operators on some non-orientable conformally flat orbifolds ⋮ An index theorem for open manifolds whose ends are warped products

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bieberbach groups and flat manifolds
• The Dirac operator on space forms of positive curvature
• Zur Abhängigkeit des Dirac-operators von der Spin-Struktur
• Zur Existenz paralleler Spinorfelder über Riemannschen Mannigfaltigkeiten

This page was built for publication: The Dirac spectrum of Bieberbach manifolds