منابع مشابه
Self-dual metrics on toric 4-manifolds: Extending the Joyce construction
Toric geometry studies manifolds M2n acted on effectively by a torus of half their dimension, T . Joyce shows that for such a 4-manifold sufficient conditions for a conformal class of metrics on the free part of the action to be self-dual can be given by a pair of linear ODEs and gives criteria for a metric in this class to extend to the degenerate orbits. Joyce and Calderbank-Pedersen use this...
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We show that solutions of the Seiberg-Witten equations lead to nontrivial estimates for the L2-norm of the Weyl curvature of a compact Riemannian 4-manifold. These estimates are then used to derive new obstructions to the existence of Einstein metrics on smooth compact 4-manifolds with a non-zero Seiberg-Witten invariant. These results considerably refine those previously obtained [21] by using...
متن کاملOn a Construction of the Twistor Spaces of Joyce Metrics
We explicitly construct the twistor spaces of some self-dual metrics with torus action given by D. Joyce. Starting from a fiber space whose fibers are compact singular toric surfaces, we apply a number of birational transformations to obtain the desired twistor spaces. Especially an important role is played by flops, a useful operation in algebraic geometry.
متن کاملProjective Models of the Twistor Spaces of Joyce Metrics
We provide a simple algebraic construction of the twistor spaces of arbitrary Joyce’s self-dual metrics on the 4-manifold H 2 × T 2 that extend smoothly to nCP, the connected sum of complex projective planes. Indeed, we explicitly realize projective models of the twistor spaces of arbitrary Joyce metrics on nCP in a CP-bundle over CP, and show that they contain the twistor spaces of H 2 × T 2 a...
متن کاملToric Integrable Metrics on Tori Are Flat
By studying completely integrable torus actions on contact manifolds we prove a conjecture of Toth and Zelditch that toric integrable geodesic flows on tori must have flat metrics.
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2013
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2013.17.2923