Let $B= \Bigg\{\begin{bmatrix} * & *&* \\ 0 & *&*\\ 0&0&* \end{bmatrix} \Bigg\}< SL(3,\mathbb C)$. What is $SL(3,\mathbb C)/B$? Do we use these facts: Borel fixed point theorem. Algebraic actions of unipotent groups are cells $U_-\cdot x_0=U_-/H$? I actually need a detailed solution because I don’t have enough background in this subject and I have […]

Question: Is the set of all conformal structures on $\mathbb{R}^n$ a manifold? Does it have a name? A pointer to a reference will suffice. Definition: A conformal structure on $\mathbb{R}^n$ is an equivalence class of inner products, with two inner products $f,g$ equivalent, $f \sim g$, if and only $f = \lambda g$ for some […]

I am learning projective geometry in my computer vision course. So, we represent a co-ordinate point in an image as a homogeneous co-ordinate as $(x,y,1)$. My professor says that if we are given two such points, $P(x_1,y_1,1)$ and $Q(x_2,y_2,1)$ then $P \times Q$ (vector product) represent the equation of this line. Any explanation to this?

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