Existence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds
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DOI: 10.1007/s00013-020-01511-x
Abstract: Using the recent work of Bettiol, we show that a first-order conformal deformation of Wilking’s metric of almost-positive sectional curvature on $$S^2\times S^3$$ yields a family of metrics with strictly positive average of sectional curvatures… read more here.
Keywords: metrics positive; existence riemannian; positive biorthogonal; simply connected ... See more keywords
New volume comparison results and applications to degeneration of Riemannian metrics
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DOI: 10.1016/j.aim.2019.06.030
Abstract: We consider a condition on the Ricci curvature involving vector fields, which is broader than the Bakry-\'Emery Ricci condition. Under this condition volume comparison, Laplacian comparison, isoperimetric inequality and gradient bounds are proven on the… read more here.
Keywords: ricci; condition; volume comparison; degeneration riemannian ... See more keywords