# Invariant Ricci-flat metrics of cohomogeneity one with Wallach spaces as principal orbits

@article{Chi2019InvariantRM, title={Invariant Ricci-flat metrics of cohomogeneity one with Wallach spaces as principal orbits}, author={Hanci Chi}, journal={Annals of Global Analysis and Geometry}, year={2019}, volume={56}, pages={361 - 401} }

We construct a continuous 1-parameter family of smooth complete Ricci-flat metrics of cohomogeneity one on vector bundles over CP2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {CP}^2$$\end{document}, HP2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts…

## 7 Citations

### Einstein Metrics of Cohomogeneity One with $${\mathbb {S}}^{4m+3}$$ as Principal Orbit

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In this article, we construct non-compact complete Einstein metrics on two infinite series of manifolds. The first series of manifolds are vector bundles with $\mathbb{S}^{4m+3}$ as principal orbit…

### Einstein Metrics of Cohomogeneity One with S 4 m +3 as Principal Orbit

- Mathematics
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: In this article, we construct non-compact complete Einstein metrics on two inﬁnite series of manifolds. The ﬁrst series of manifolds are vector bundles with S 4 m +3 as principal orbit and HP m as…

### Spin(7) Metrics of Cohomogeneity One with Aloff–Wallach Spaces as Principal Orbits

- MathematicsThe Journal of Geometric Analysis
- 2022

In this article, we construct two continuous 1-parameter family of non-compact Spin(7) metrics with both chiralities, with the principal orbit an Aloff–Wallach space Nk,l and the singular orbit CP.…

### Cohomogeneity-one solitons in Laplacian flow: local, smoothly-closing and steady solitons

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We initiate a systematic study of cohomogeneity-one solitons in Bryant’s Laplacian flow of closed G2–structures on a 7-manifold, motivated by the problem of understanding finite-time singularities of…

### Optimal coordinates for Ricci-flat conifolds

- Mathematics
- 2022

We compute the indicial roots of the Lichnerowicz Laplacian on Ricci-flat cones and give a detailed description of the corresponding radially homogeneous tensor fields in its kernel. For a Ricci-flat…

### SMOOTHNESS CONDITIONS IN COHOMOGENEITY ONE MANIFOLDS

- MathematicsTransformation Groups
- 2020

We present an efficient method for determining the conditions that a metric on a cohomogeneity one manifold, defined in terms of functions on the regular part, needs to satisfy in order to extend…

### SMOOTHNESS CONDITIONS IN COHOMOGENEITY ONE MANIFOLDS

- MathematicsTransformation Groups
- 2020

We present an efficient method for determining the conditions that a metric on a cohomogeneity one manifold, defined in terms of functions on the regular part, needs to satisfy in order to extend…

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