## A easy question of Riemannian geometry [closed]

If N,M∈P are totally geodesic submanifolds,show that each component of N∩M is a submanifold which is a totally geodesic.

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Yes, this is an easy question. – Igor Rivin Jan 3 2011 at 16:16
Take a point $p\in M\cap N$ and think about the exponential map of ambient manifold at $p$. What are images of $T_{M,p}$ etc. under this map? – Donu Arapura Jan 3 2011 at 16:18