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This is a simple terminology question. Let $S$ be a (let's say smooth) surface in $\mathbb{R}^3$, and $p$ a point on $S$. Suppose the principle curvatures $\kappa_1$ and $\kappa_2$ at $p$ are both negative. I am imagining $p$ sitting at the bottom of a dent in the surface. Is there an accepted term to describe such a point? The difficulty is that the Gaussian curvature $\kappa_1 \kappa_2$ is positive, so intrinsically $p$ is no different than if it were on a bump rather than a dent. I could make up my own term of course, e.g., valley point or cup point, but I'd rather follow convention.

Thanks!

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    I've never come across specific terminology for this situation. I think if $p$ is really at a "dent" in the surface, not only should the Gauss curvature be positive there, but it should decrease (roughly with the distance to $p$) and become negative near $p$.2010-09-12
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    The only term I could find is "elliptical" point (the signs of $\kappa_1$ and $\kappa_2$ are the same), so maybe you can just invent a new adjective to add to "elliptical".2010-09-12
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    @Ryan: Yes, I see there are constraints nearby. @JM: Ah, _elliptical_! I didn't know that term. Your suggestion of modifying that term is perhaps my solution. Thanks!2010-09-12

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