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Results tagged with complex-geometry
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user 171387
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.
5
votes
1
answer
428
views
Isometric immersion of $\mathbb H^2$ into $\mathbb R^\infty$ built by Bieberbach
I'm analyzing the following isometric immersion of $(\mathbb H^2,g_D)$ in $(\ell^2,g_\infty)$ given by $f(x,y)=(x_1,x_2,\dots,x_{2m-1},x_{2m},\dots)$ with
\begin{align}\label{5.1}
x_{2m-1}=\color{ …
- 143
5
votes
Accepted
Isometric immersion of $\mathbb H^2$ into $\mathbb R^\infty$ built by Bieberbach
After a few tries I got the following:
Instead of taking real variable I take complex variable, that is let $z_m=\dfrac{\color{red}{2}z^m}{\sqrt{m}}$, donde $z_m=x_{2m-1}+ix_{2m}$. Then $dz_m=\color{r …
- 143