A given curve is an helix?

Question

Given the vectorial function $$\vec{r}(t)=\cos(t)\,\mathbf{i}+\sin(t)\,\mathbf{j}+\ln (\cos(t))\,\mathbf{k},\quad 0\leq t\leq \pi/4$$ How can I justify that a curve is an helix? How do I express it mathematically? Does it have anything to do with the curvature? I calculated the length $s(t)$ of the curve $C$ as a function of $t$. I also expressed the curve $C$ as a function of the arc length $s$ and calculated the intrinsic trihedron $(\vec{u}_T(s), \vec{u}_N(s), \vec{u}_B(s))$ as a function of $s$. And finally I found the curvature $\kappa (s)$ as a function of $s$.