Negative sectional curvature and the product complex structure

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dc.creatorSeshadri, Harish
dc.date2006-02-14
dc.date.accessioned2026-07-07T07:03:24Z
dc.date.available2026-07-07T07:03:24Z
dc.descriptionWe prove that a product complex manifold cannot admit a complete Kähler metric with sectional curvature $K<c<0$ and Ricci curvature $Ric > d$, where $c$ and $d$ are constants. In particular, a product domain in $\C$ cannot cover a compact Kähler manifold with negative sectional curvature. On the other hand, we observe that there are complete Kähler metrics with negative sectional curvature on $\C$. Hence the upper sectional curvature bound is necessary.
dc.description6 Pages. To appear in Mathematical Research Letters
dc.identifierhttps://arxiv.org/abs/math/0602289
dc.identifierhttp://arxiv.org/abs/math/0602289
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/108956
dc.subjectDifferential Geometry
dc.subjectComplex Variables
dc.subject53C21
dc.titleNegative sectional curvature and the product complex structure
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