## Some geometric facts of Cylinder

Let be a cylinder with radius 1.

Pull back the metric of to cylinder . Then cylinder is locally flat Riemanian manifold. Its curvature tensor is 0 and thus the sectional curvature is also 0.

If has non-positive sectional curvature, then any point does not have conjugate points.

Suppose . Then . Actually, any two points can be connected by infinitely many geodesics. But the is the cylinder except a line apposite to .

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