TY - JOUR
T1 - Invariant Ricci-flat metrics of cohomogeneity one with Wallach spaces as principal orbits
AU - Chi, Hanci
N1 - Publisher Copyright:
© 2019, Springer Nature B.V.
PY - 2019
Y1 - 2019
N2 - We construct a continuous 1-parameter family of smooth complete Ricci-flat metrics of cohomogeneity one on vector bundles over CP2, HP2 and OP2 with respective principal orbits G / K the Wallach spaces SU(3) / T2, Sp(3) / (Sp(1)Sp(1)Sp(1)) and F4/ Spin (8). Almost all the Ricci-flat metrics constructed have generic holonomy. The only exception is the complete G2 metric discovered in Bryant and Salamon (Duke Math J 58(3):829–850, 1989) and Gibbons et al. (Commun Math Phys 127(3):529–553, 1990). It lies in the interior of the 1-parameter family on ⋀-2CP2. All the Ricci-flat metrics constructed have asymptotically conical limits given by the metric cone over a suitable multiple of the normal Einstein metric on G / K.
AB - We construct a continuous 1-parameter family of smooth complete Ricci-flat metrics of cohomogeneity one on vector bundles over CP2, HP2 and OP2 with respective principal orbits G / K the Wallach spaces SU(3) / T2, Sp(3) / (Sp(1)Sp(1)Sp(1)) and F4/ Spin (8). Almost all the Ricci-flat metrics constructed have generic holonomy. The only exception is the complete G2 metric discovered in Bryant and Salamon (Duke Math J 58(3):829–850, 1989) and Gibbons et al. (Commun Math Phys 127(3):529–553, 1990). It lies in the interior of the 1-parameter family on ⋀-2CP2. All the Ricci-flat metrics constructed have asymptotically conical limits given by the metric cone over a suitable multiple of the normal Einstein metric on G / K.
KW - Cohomogeneity one manifold
KW - G holonomy
KW - Noncompact Ricci-flat manifold
UR - http://www.scopus.com/inward/record.url?scp=85068320513&partnerID=8YFLogxK
U2 - 10.1007/s10455-019-09671-y
DO - 10.1007/s10455-019-09671-y
M3 - Article
AN - SCOPUS:85068320513
SN - 0232-704X
JO - Annals of Global Analysis and Geometry
JF - Annals of Global Analysis and Geometry
ER -