Fefferman metric in several complex variables
E537774
The Fefferman metric in several complex variables is a canonical Lorentz–Kähler-type metric associated with strictly pseudoconvex domains, fundamental in the study of CR geometry and the boundary behavior of holomorphic functions.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Fefferman–Kohn theory in several complex variables | 1 |
Statements (32)
| Predicate | Object |
|---|---|
| instanceOf |
Lorentz–Kähler-type metric
ⓘ
canonical metric ⓘ geometric structure ⓘ |
| associatedWith |
CR manifolds
ⓘ
boundary behavior of holomorphic functions ⓘ strictly pseudoconvex domains ⓘ |
| captures | CR curvature invariants ⓘ |
| definedOn |
circle bundle over the boundary of a strictly pseudoconvex domain
ⓘ
total space of the canonical circle bundle of a CR manifold ⓘ |
| dependsOn | defining function of a strictly pseudoconvex domain ⓘ |
| dimensionContext | complex dimension at least 2 ⓘ |
| field |
CR geometry
ⓘ
complex differential geometry ⓘ several complex variables ⓘ |
| generalizes | Bergman metric behavior near the boundary ⓘ |
| hasSignature | Lorentzian ⓘ |
| hasStructure | Kähler-like structure ⓘ |
| introducedBy | Charles Fefferman NERFINISHED ⓘ |
| invariantUnder | CR automorphisms ⓘ |
| isCanonical | true ⓘ |
| relatedTo |
CR Yamabe problem
NERFINISHED
ⓘ
Tanaka–Webster connection NERFINISHED ⓘ ambient metric construction in conformal geometry ⓘ pseudo-Hermitian geometry ⓘ |
| usedFor |
analyzing the Bergman kernel
ⓘ
constructing CR invariant differential operators ⓘ studying CR invariants ⓘ studying the Szegő kernel ⓘ studying the asymptotic expansion of the Bergman kernel ⓘ studying the boundary regularity of biholomorphic mappings ⓘ |
| usedIn |
analysis on strictly pseudoconvex domains
ⓘ
microlocal analysis of the \ ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Fefferman–Kohn theory in several complex variables