Conformally Flat Structures and Hyperbolic Structures
نویسنده
چکیده
We define an abelian group, the conformal cobordism group of hyperbolic structures, which classifies the hyperbolic structures according to whether it bounds a (higher dimensional) conformally flat structure in a conformally invariant way. We then construct a homomorphism from this group to the circle group, using the eta invariant. The homomorphism can be highly nontrivial. It remains an interesting question of how to compute this group.
منابع مشابه
Eta Invariant and Conformal Cobordism
In this note we study the problem of conformally flat structures bounding conformally flat structures and show that the eta invariants give obstructions. These lead us to the definition of an Abelian group, the conformal cobordism group, which classifies the conformally flat structures according to whether they bound conformally flat structures in a conformally invariant way. The eta invariant ...
متن کاملConformally Parallel G2 Structures on a Class of Solvmanifolds
Starting from a 6-dimensional nilpotent Lie group N endowed with an invariant SU(3) structure, we construct a homogeneous conformally parallel G2-metric on an associated solvmanifold. We classify all half-flat SU(3) structures that endow the rank-one solvable extension of N with a conformally parallel G2 structure. By suitably deforming the SU(3) structures obtained, we are able to describe the...
متن کاملConformally Flat Pencils of Metrics, Frobenius Structures and a Modified Saito Construction
The structure of a Frobenius manifold encodes the geometry associated with a flat pencil of metrics. However, as shown in the authors’ earlier work [1], much of the structure comes from the compatibility property of the pencil rather than from the flatness of the pencil itself. In this paper conformally flat pencils of metrics are studied and examples, based on a modification of the Saito const...
متن کاملMetric Conformal Structures and Hyperbolic Dimension
For any hyperbolic complex X and a ∈ X we construct a visual metric ď = ďa on ∂X that makes the Isom(X)-action on ∂X bi-Lipschitz, Möbius, symmetric and conformal. We define a stereographic projection of ďa and show that it is a metric conformally equivalent to ďa. We also introduce a notion of hyperbolic dimension for hyperbolic spaces with group actions. Problems related to hyperbolic dimensi...
متن کاملOptimization of Thermal Instability Resistance of FG Flat Structures using an Improved Multi-objective Harmony Search Algorithm
This paper presents a clear monograph on the optimization of thermal instability resistance of the FG (functionally graded) flat structures. For this aim, two FG flat structures, namely an FG beam and an FG circular plate, are considered. These structures are assumed to obey the first-order shear deformation theory, three-parameters power-law distribution of the constituents, and clamped bounda...
متن کامل