I have a complete and homogeneously regular Riemannian manifold $M$, embedded isometrically in a Euclidean space $\mathbb{R}^n$. And $N \subset M$ is a closed and embedded submanifold, not necessarily connected.
I know that the second fundamental form of $M$ and $N$ are bounded, with norm less than or equal to $1/16$. I know that the sectional curvature of $M$ is at most $1/64$.
Is there a way (with this information) to calculate the sectional curvature of $N$? Or will they both have the same curvature?
I scaled the metric, where the sectional curvature is multiplied by a constant $\lambda^{-1}$.