There is a closed connected orientable smooth three-manifold that carries a smooth metric without conjugate points but carries no smooth metric of everywhere nonpositive sectional curvature.
There is a closed connected orientable smooth three-manifold that carries a smooth metric without conjugate points but carries no smooth metric of everywhere nonpositive sectional curvature.
There is a closed connected orientable smooth three-manifold that carries a smooth metric without conjugate points but carries no smooth metric of everywhere nonpositive sectional curvature.
If correct, separates absence of conjugate points from the existence of a nonpositively curved metric in the first possible dimension.
Does a closed manifold without conjugate points always admit a nonpositively curved metric?
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OpenAI reports a three-manifold without conjugate points or a nonpositive-curvature metric
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