Picture below is from Lectures on mean curvature flows.
What is the mean of $\alpha$ and $\beta$ ? As definition, $g_{ij}=\langle \partial_i X , \partial _j X \rangle$. Why there are $\alpha$ and $\beta$ ?
Besides, how to understand the Laplace operator is degenerate on the tangential directions? I can't understand the red line. In my view , a operator degenerate mean the determinant of coefficient of 2-order term equal to zero at some point.
