Weakly almost-Fuchsian manifolds are nearly-Fuchsian and quasi-Fuchsian, and nearly-Fuchsian manifolds need not be almost-Fuchsian.
Positively curved surfaces in the three-sphere
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Weakly almost-Fuchsian manifolds are nearly-Fuchsian
Weakly almost-Fuchsian manifolds are nearly-Fuchsian and quasi-Fuchsian, and nearly-Fuchsian manifolds need not be almost-Fuchsian.