Vanishing of top-degree Pontryagin class products obstructs purely electric or magnetic Weyl curvature on compact 4k-manifolds.
Totally umbilic Riemannian foliations.Michigan Math
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Survey of known results on the bottom of the spectrum of the Hodge Laplacian on complete noncompact Kähler manifolds, including upper bounds under curvature assumptions and rigidity theorems.
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A Pontryagin class obstruction for purely electric and purely magnetic Weyl curvature tensors
Vanishing of top-degree Pontryagin class products obstructs purely electric or magnetic Weyl curvature on compact 4k-manifolds.
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Bottom of the spectrum of complete noncompact K\"{a}hler manifolds
Survey of known results on the bottom of the spectrum of the Hodge Laplacian on complete noncompact Kähler manifolds, including upper bounds under curvature assumptions and rigidity theorems.