# Tagged Questions

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### Comparing the norm of a trace of a curvature tensor with the full norm

Let $V$ and $E$ be complex vector spaces of dimensions $n$ and $r$, equipped with hermitian inner products $\omega$ and $h$ respectively. Let $R$ be a curvature-type tensor, that is an element of ...
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### Linear Complex Structure and Kähler Angles

I am trying to read Donaldson's paper on symplectic submanifolds http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jdg/1214459407 and am getting a bit ...
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### Alternative Almost Complex Structures

Let $V$ be a real vector space. An almost complex structure on $V$ is a map $J : V \to V$ such that $J^2 = -\mathrm{id}_V$. An almost complex structure gives $V$ the structure of a complex vector ...
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### Cross product in complex vector spaces

When inner product is defined in complex vector space, conjugation is performed on one of the vectors. What about is the cross product of two complex 3D vectors? I suppose that one possible ...
Let $M\subset \mathbb C^2$ be a hypersurface defined by $F(z,w)=0$. Then for some point $p\in M$, I've \text{ rank of }\left( \begin{array}{ccc} 0 &\frac{\partial F}{\partial z} ...
I came across one sentence below, I am not able to see it... Any comment suggestion, reference is welcome. Thanks in advance. "Let $V$ be a finite dimensional inner product space. The ...