Talk:Sectional curvature

Question
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°".

patrick flaherty 07:37, 7 January 2006


 * 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 41.145.109.129 (talk) 19:05, 30 November 2009 (UTC)

Relation to Riemann tensor
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)

The 2-dimensional case
The first sentence of this article is: In Riemannian geometry, the sectional curvature is one of the ways to describe the curvature of Riemannian manifolds with dimension greater than 2.

However, the section curvature also seems to make sense in 2 dimensions, see https://math.stackexchange.com/questions/1832106/sectional-curvature-of-2-manifold.

Shouldn't "greater than 2" be corrected to "greater than 1"? 89.135.24.74 (talk) 04:21, 2 July 2021 (UTC)