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Apr 16, 2017 at 5:22 comment added Deane Yang Anton, why? If he wants the second order term in both $x$ and $t$, I agree. I was assuming he wanted only the second order term in $t$ only with $x$ fixed.
Apr 15, 2017 at 17:57 comment added Deane Yang This is not hard to generalize to submanifolds of arbitrary codimension $1 \le k \le n$. The details are in the paper by Heintze and Karcher.
Apr 15, 2017 at 17:50 history answered Deane Yang CC BY-SA 3.0