Communications in Analysis and Geometry

Volume 23 (2015)

Number 3

A family of steady Ricci solitons and Ricci-flat metrics

Pages: 611 – 638

DOI: http://dx.doi.org/10.4310/CAG.2015.v23.n3.a5

Authors

M. Buzano (Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada)

A. S. Dancer (Jesus College, Oxford University, United Kingdom)

M. Wang (Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada)

Abstract

We produce new non-Kähler complete steady gradient Ricci solitons whose asymptotics combine those of the Bryant solitons and the Hamilton cigar. The underlying manifolds are of the form $\mathbb{R}^2 \times M_2 \times \cdots \times M_r$ where $M_i$ are arbitrary Einstein manifolds with positive scalar curvature. On the same spaces we also obtain a family of complete non-Kähler Ricci-flat metrics with asymptotically locally conical asymptotics. Among these new Ricci-flat and soliton examples are pairs with dimension $4m + 3$ which are homeomorphic but not diffeomorphic.

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Published 30 January 2015