17 citations · 23 across the 4 of their papers we have counts for
14 papers · 1 filter
Sasakian Geometry, Hypersurface Singularities, and Einstein Metrics
Charles P. Boyer, Krzysztof Galicki
We review our study of Sasakian geometry as an agent for proving the existence of Einstein metrics on odd dimensional manifolds. Particular emphasis is given to the Sasakian struct…
Einstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15
Charles P. Boyer, Krzysztof Galicki, János Kollár +1
In a recent article the first three authors proved that in dimension all homotopy spheres that bound parallelizable manifolds admit Einstein metrics of positive scalar curva…
Einstein Metrics on Spheres
Charles P. Boyer, Krzysztof Galicki, János Kollár
We prove the existence of an abundance of new Einstein metrics on odd dimensional spheres including exotic spheres, many of them depending on continuous parameters. The number of f…
New Einstein Metrics on 8#(S^2 times S^3)
Charles P. Boyer, Krzysztof Galicki
We show that #8(S^2 times S^3) admits two 8-dimensional complex families of inequivalent non-regular Sasakian-Einstein structures. These are the first known non-regular Sasakian-Ei…
Rational Homology 5-Spheres with Positive Ricci Curvature
Charles P. Boyer, Krzysztof Galicki
We prove that for every integer k>1 there is a simply connected rational homology 5-sphere with spin such that $\scriptstyle{H_2(M^5_k,\bbz)}$ has order $\scr…
Sasakian Geometry, Homotopy Spheres and Positive Ricci Curvature
Charles P. Boyer, Krzysztof Galicki, Michael Nakamaye
We discuss the Sasakian geometry of odd dimensional homotopy spheres. In particular, we give a completely new proof of the existence of metrics of positive Ricci curvature on exoti…