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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
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Open questions in Riemannian geometry
There is also "Review of Geometry and Analysis" by S.-T. Yau (Asian Journal of Mathematics, vol. 4, no. 1, pp. 235-278, March 2000), where he discusses many big open problems in Riemannian geometry, s …