Rigidity result classifies torus bundles with affine structure groups under b1(M) - b1(N) = dim M - dim N, with splitting conditions for principal torus bundles.
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Slow relative volume growth on complete manifolds with nonnegative Ricci curvature implies almost abelian or finite fundamental groups.
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Structure of Torus Fibration Under the First Betti Number Restriction
Rigidity result classifies torus bundles with affine structure groups under b1(M) - b1(N) = dim M - dim N, with splitting conditions for principal torus bundles.
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Complete manifolds with nonnegative Ricci curvature and slow relative volume growth
Slow relative volume growth on complete manifolds with nonnegative Ricci curvature implies almost abelian or finite fundamental groups.