582 research outputs found
Certain 4-manifolds with non-negative sectional curvature
In this paper, we study certain compact 4-manifolds with non-negative
sectional curvature . If is the scalar curvature and is the
self-dual part of Weyl tensor, then it will be shown that there is no metric
on with both (i) and (ii) .
We also investigate other aspects of 4-manifolds with non-negative sectional
curvature. One of our results implies a theorem of Hamilton: ``If a
simply-connected, closed 4-manifold admits a metric of non-negative
curvature operator, then is one of , and ".
Our method is different from Hamilton's and is much simpler. A new version of
the second variational formula for minimal surfaces in 4-manifolds is proved
Pseudo-Einstein and Q-flat metrics with eigenvalue estimates on CR-hypersurfaces
Let be the smooth boundary of a bounded strongly pseudo-convex
domain in a complete Stein manifold . Then (1) For ,
admits a pseudo-Eistein metric; (2) For , admits
a Fefferman metric of zero CR Q-curvature; and (3) for a compact strictly
pseudoconvex CR embeddable 3-manifold , its CR Paneitz operator is a
closed operator
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