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- Title
Positive Einstein metrics with $\mathbb {S}^{4m+3}$ as the principal orbit.
- Authors
Chi, Hanci
- Abstract
We prove that there exists at least one positive Einstein metric on $\mathbb {HP}^{m+1}\sharp \overline {\mathbb {HP}}^{m+1}$ for $m\geq ~2$. Based on the existence of the first Einstein metric, we give a criterion to check the existence of a second Einstein metric on $\mathbb {HP}^{m+1}\sharp \overline {\mathbb {HP}}^{m+1}$. We also investigate the existence of cohomogeneity-one positive Einstein metrics on $\mathbb {S}^{4m+4}$ and prove the existence of a non-standard Einstein metric on $\mathbb {S}^8$.
- Subjects
EINSTEIN, Albert, 1879-1955; ORBITS (Astronomy); EINSTEIN manifolds
- Publication
Compositio Mathematica, 2024, Vol 160, Issue 5, p1004
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X24007073