Mathematische Annalen

, Volume 325, Issue 3, pp 485–524

On the geometry of Sasakian-Einstein 5-manifolds

  • Charles P. Boyer
  • Krzysztof Galicki
  • Michael Nakamaye

DOI: 10.1007/s00208-002-0388-3

Cite this article as:
Boyer, C., Galicki, K. & Nakamaye, M. Math. Ann. (2003) 325: 485. doi:10.1007/s00208-002-0388-3

Abstract

 On simply connected five manifolds Sasakian-Einstein metrics coincide with Riemannian metrics admitting real Killing spinors which are of great interest as models of near horizon geometry for three-brane solutions in superstring theory [24]. We expand on the recent work of Demailly and Kollár [14] and Johnson and Kollár [20] who give methods for constructing Kähler-Einstein metrics on log del Pezzo surfaces. By a previous result of the first two authors [9], circle V-bundles over log del Pezzo surfaces with Kähler-Einstein metrics have Sasakian-Einstein metrics on the total space of the bundle. Here these simply connected 5-manifolds arise as links of isolated hypersurface singularities which by the well known work of Smale [36] together with [11] must be diffeomorphic to S5#l(S2×S3). More precisely, using methods from Mori theory in algebraic geometry we prove the existence of 14 inequivalent Sasakian-Einstein structures on S2×S3 and infinite families of such structures on #l(S2×S3) with 2≤l≤7. We also discuss the moduli problem for these Sasakian-Einstein structures.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Charles P. Boyer
    • 1
  • Krzysztof Galicki
    • 1
  • Michael Nakamaye
    • 1
  1. 1.Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico, 87131, USAUS