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$M$ is riemannian manifold, if a smooth function $f$ satisfies $\left| \operatorname{grad}\ f \right|=1,$ then prove the integral curves of $\operatorname{grad}\ f$ are geodesics.

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    So ... what is your question? What effort have you put into it?2012-03-13
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    prove why the integral curves of $grad\ f$ are geodesics2012-03-13
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    The gradient of a function is a vector. What do you mean by it equalling 1?2012-03-13
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    sorry, I've edited this question.For this time I can't see the conversion of Latex in my webpage,I can't check questions clearly.2012-03-13
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    Duplicate of https://math.stackexchange.com/questions/16911/integral-curves-of-the-gradient2018-05-10

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