Geometriae Dedicata

, Volume 101, Issue 1, pp 93–102

On Positive Sasakian Geometry

  • Charles P. Boyer
  • Krzysztof Galicki
  • Michael Nakamaye
Article

DOI: 10.1023/A:1026363529906

Cite this article as:
Boyer, C.P., Galicki, K. & Nakamaye, M. Geometriae Dedicata (2003) 101: 93. doi:10.1023/A:1026363529906

Abstract

A Sasakian structure \(\mathcal{S}\)=(\xi,\eta,\Phi,g) on a manifold Mis called positiveif its basic first Chern class c1(\(\mathcal{F}\)ξ) can be represented by a positive (1,1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature. This provides us with a new technique for proving the existence of positive Ricci curvature metrics on certain odd dimensional manifolds. As an example we give a completely independent proof of a result of Sha and Yang that for every nonnegative integer kthe 5-manifolds k#(S2×S3) admits metrics of positive Ricci curvature.

Fano varietiespositive Ricci curvatureSasakian geometry

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Charles P. Boyer
    • 1
  • Krzysztof Galicki
    • 1
  • Michael Nakamaye
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueU.S.A.