I have the following question:
Let $M\subset R^3$ be a regular surface and $A\in M$ a point where the gauss curvature $K$ and the mean curvature $H$ satisfy $K\neq 0, H=0$. Also, let $\alpha, \beta:(-1,1)\to M$ be regular curves such that $\alpha(0)=\beta(0)=A$ and the angle between their tangents at this point is not $0$. Also, $\alpha''(0),\beta''(0)\in T_AM$. Find the angle between the curves in $A$.
I can conclude from the condition on the curvatures that $K<0$. I am also familiar with the first and second fundamental forms, sectional curvature and curvature operator and "theorema egregium", Though I can't seem to find a direction to a solution.
Thanks in advance.