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Results tagged with conformal-geometry
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user 121820
18
votes
Accepted
Geometric interpretation of the Weyl tensor?
There is such an interpretation, with a few caveats. Essentially, there is a canonical connection on a certain vector bundle for which the "principal part" of the curvature is the Weyl tensor in dime …
- 1,713
10
votes
Accepted
Definition of the conformal metric
Let $(M,[g])$ be a conformal manifold;
i.e. $(M,g)$ is a Riemannian manifold and $[g] = \{ u^2g \mathrel{}:\mathrel{} u \in C^\infty(M), u>0 \}$ is the set of Riemannian metrics conformal to $g$.
It i …
- 1,713
5
votes
Is the conformal compactification of $M \setminus \{ p \}$ unique?
Theorem 1.4 in C. Frances' preprint "Rigidity at the boundary for conformal structures and other Cartan geometries" asserts that the geodesic compactification is unique (up to conformal diffeomorphism …
- 1,713
3
votes
Accepted
Yamabe operator, conformal transformations and square of the Dirac operator
The discrepancy comes from the fact that the square of the Dirac operator is in general not conformally covariant. There are ways to modify powers of the Dirac operator to get a conformally covariant …
- 1,713
2
votes
Accepted
Expansion of metric near boundary of 3 dimensional Poincaré-Einstein/hyperbolic manifolds
This is only an answer to the request for references about the expansion and an interpretation of $h_2$ from the standpoint of the metric $x^2g$.
Theorem 7.4 in the book The Ambient Metric proves that …
- 1,713