Consider a Riemannian manifold $M$ with sectional curvatures $K\ge 0$ and let $\Pi$ be a 2-plane in the tangent space of $M$ at a point $p$. In a small enough neighborhood $U$ of 0 the exponential map will be a diffeomorphism and $S=\text{exp}(U\cap \Pi)$ will be an open surface in $M$. The Gaussian curvature of this surface at $p$ is the sectional curvature of $M$ corresponding to the 2-plane $\Pi$.

My question is this: can anything be said about the Gaussian curvature of $S$ at points other than $p$? For example, is it still nonnegative?