PeterDonis
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A.T. said:Are you sure about this? Here they say Gaussian curvature of Flamm's paraboloid is negative
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To me it looks like it does exactly that.
WannabeNewton said:You can picture this for Flamm's paraboloid and see that there is one direction where the curve would locally turn away from the normal and another direction where it would locally turn towards it (the principal directions); it isn't too different locally from a hyperbolic paraboloid.
Yes, I see what you mean. I'm working on computing the principal curvatures from the metric to verify this.