$M$ 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.
A smooth function f satisfies $\left|\operatorname{ grad}\ f \right|=1$ ,then the integral curves of $\operatorname{grad}\ f$ are geodesics
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differential-geometry
riemannian-geometry
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5So ... what is your question? What effort have you put into it? – 2012-03-13
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0prove why the integral curves of $grad\ f$ are geodesics – 2012-03-13
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0The gradient of a function is a vector. What do you mean by it equalling 1? – 2012-03-13
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0sorry, 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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0Duplicate of https://math.stackexchange.com/questions/16911/integral-curves-of-the-gradient – 2018-05-10