Hi. Sectional Curvature. I can see that a number of people have edited this page over time. All of them, I would assume, more knowledgeable in this area than myself.
Still. I'm a programmer; am far from completely uneducated in mathematics; and consider myself, say, a technical layman.
My question. The explanation of sectional curvature that appears currently is no doubt general (and hopefully correct). I wouldn't however consider it particularly penetrable myself.
Would it be possible to add something to the effect of:
"positively curved space is such that if you were to 'lay' a triangle onto the surface, the sum of its angles would be greater than 180°. Negatively curved space implies the opposite: triangles where the sum of the angles is less than 180°".
The point is that sectional curvature is but one realisation of the concept of curvature in general, and hence this article should be seen as more specific to the topic - what you have suggested, though more than sensible, would be more appropriate in the general article on curvature (spec. Ricci) and the more lay introduction ot non-Euclidean geometry. —Preceding unsigned comment added by 188.8.131.52 (talk) 19:05, 30 November 2009 (UTC)
I think the page needs an explanation of the relationship between the Riemann tensor and the sectional curvature. That's what I came here looking for...
Shambolic Entity 00:55, 28 July 2006 (UTC)