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Gravitational instantons of constant curvature

John G Ratcliffe and Steven T Tschantz

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In this paper, we classify all closed flat 4-manifolds that have a reflective symmetry along a separating totally geodesic hypersurface. We also give examples of small-volume hyperbolic 4-manifolds that have a reflective symmetry along a separating totally geodesic hypersurface. Our examples are constructed by gluing together polytopes in hyperbolic 4-space.


PACS

95.30.Sf Relativity and gravitation

98.80.-k Cosmology

04.60.Pp Loop quantum gravity, quantum geometry, spin foams

02.40.-k Geometry, differential geometry, and topology

MSC

14J35 4-folds

85A40 Cosmology (For relativistic cosmology, see 83F05)

53D25 Geodesic flows

14J70 Hypersurfaces

Subjects

Mathematical physics

Gravitation and cosmology

Astrophysics and astroparticles

Dates

Issue 9 (September 1998)

Received 10 June 1998



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