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Results tagged with dg.differential-geometry
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user 94640
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
2
votes
1
answer
208
views
$L^{2}$ Betti number
Let $\tilde{X}$ be a non-compact oriented, Riemannian manifold adimits a smooth metric $\tilde{g}$ on which a discrete group $\Gamma$ of orientation-preserving isometrics acts freely so that the quoti …
- 61
1
vote
0
answers
98
views
Is a manifold $R^{+}\times X$ with metric $dt^{2}+t^{2}\rm{g}_{X}$ complete?
The cone $C(X)$ over a complete manifold $X$ is defined as $R^{+}\times X$ admits the metric $dt^{2}+t^{2}g_{X}$. The manifold $C(X)$ is conformal to $Cyl(X):=\{R^{+}\times X, dt^{2}+g_{X})$. Followin …
- 61
2
votes
0
answers
141
views
Kähler manifold with a global potential
If $(X^{n},\omega)$ is a complete Kähler manifold with a global potential, i.e. $\omega=i\partial\bar{\partial}f$. There are many articles study the $L^{2}$-cohomology of $X$ under some conditions on …
- 61
1
vote
1
answer
179
views
stable bundle on Calabi-Yau 3-fold
Let $E$ be a $G$-bundle over a compact Calabi-Yau 3-fold, $G$ is semi-simple,compact Lie group. If $E$ is a stable bundle, is the first Chern class of $E$ always zero?
- 61