Smooth structures and Einstein metrics on CP2#5,6,7CP2

• Autores: Rares Rasdeaconu, Ioana Suvaina
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 147, Nº 2, 2009, págs. 409-417
• Idioma: inglés
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• Resumen

  • We show that each of the topological 4-manifolds , for k = 5, 6, 7, 8 admits a smooth structure which has an Einstein metric of scalar curvature s > 0, a smooth structure which carries an Einstein metric with s < 0 and infinitely many non-diffeomorphic smooth structures which do not admit Einstein metrics. We also exhibit new examples of higher dimensional manifolds carrying Einstein metrics of both positive and negative scalar curvature.