diff --git a/main.tex b/main.tex index 408a36d..cbe80ef 100644 --- a/main.tex +++ b/main.tex @@ -98,12 +98,12 @@ code-for-last-col = \color{blue} \begin{frame}[fragile]{CMB Anisotropy of Homogeneous Spherical Spaces} \begin{itemize} - \item Manifolds $M := \mathbb{S}^3 /_ \sim$ where $\sim $ identifies the orbits of finite $H \leq SO(4)$ finite + \item Manifolds $\textcolor{blue}{M} := \mathbb{S}^3 /_ \sim$ where $\sim $ identifies the orbits of finite $H \leq SO(4)$ finite \item Helmholtz equation on $M$ given by - $$(\Delta + E_\beta^M)\psi_\beta^{M, i} = 0$$ + $$(\Delta + E_\textcolor{red}{\beta}^M)\psi_\textcolor{red}{\beta}^{M, i} = 0$$ - \item In fact $E_\beta^m = \beta^2-1$ for $\beta \in \mathbb{N}$ we call $\beta$ a wave number + \item In fact $E_\textcolor{red}{\beta}^m = \textcolor{red}{\beta}^2-1$ for $\textcolor{red}{\beta} \in \mathbb{N}$ we call $\textcolor{red}{\beta}$ a wave number \item The set of all possible wave numbers [for which there exists a non-zero solution] depends on $H$ @@ -154,7 +154,8 @@ code-for-last-col = \color{blue} \begin{itemize} \item Multi-connected space: it has non-contractable loops - \item Inhomogeneous space: it does not look the same from every point in space + \item Inhomogeneous space: it does not look identical from every point in space + \item \end{itemize} \end{frame}