# Is this function convex ? (Riemannian geometry)

Let $$f:Mtomathbb R$$ be a geodesically convex function on a Riemannian manifold $$M$$, assumed to have nonpositive sectional curvature.

Fix $$x_0in M$$ and let $$g:T_{x_0}Mtomathbb R$$ the map defined by $$g(u)=f(exp_{x_0}(u))$$.

Is $$g$$ convex ?