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Results tagged with complex-geometry
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user 90154
Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
8
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Examples of manifolds that do not admit scalar flat metrics
The Kazdan-Warner trichotomy states that for $n\ge 3$, a compact $n$-manifold falls into one of three categories:
(A) Every (smooth) function is a scalar curvature.
(B) The manifold is strongly scal …
- 738
4
votes
Accepted
Examples of manifolds that do not admit scalar flat metrics
Christos Mantoulidis showed me how to construct examples in (C) in all dimensions. Namely, if $\Sigma_g^2$ denotes a genus $g$ surface with $g\ge 2$, then $\Sigma_g^2\times T^{n-2}$ does is in class ( …
- 738