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Let S be a simply connected complete surface with Gauss curvature (Kleq0) everywhere.
Suppose that S is a simply connected complete surface with Gauss curvature (Kleq0) everywhere.
Let S be a simply connected complete surface with Gauss curvature K, (Kleq-alpha^{2}), (alpha>0).
Let S be a simply connected complete surface with Gauss curvature K, (-beta^{2}leq Kleq0) everywhere.
Suppose that S is a simply connected complete surface with Gauss curvature K, (-beta^{2}leq Kleq0) everywhere.
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Notice that the only manifolds on the list supplied by Theorem 5.2 that are both simply connected and complete are those appearing in (ii).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com