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}
}
  • Hanci Chi
  • Published 5 March 2019
  • Mathematics
  • Annals of Global Analysis and Geometry
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… 

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

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

: 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

  • Hanci Chi
  • Mathematics
    The 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

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

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

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

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

References

SHOWING 1-10 OF 41 REFERENCES

Einstein metrics on $S^{2}$-bundles

Abstract. New Einstein metrics are constructed on the associated ${\Bbb R}{\Bbb P}^2$, $S^2$, and ${\Bbb R}^2$-bundles of principal circle bundles with base a product of Kähler-Einstein manifolds

Infinitely many new families of complete cohomogeneity one G$_2$-manifolds: G$_2$ analogues of the Taub–NUT and Eguchi–Hanson spaces

We construct infinitely many new 1-parameter families of simply connected complete noncompact G_2-manifolds with controlled geometry at infinity. The generic member of each family has so-called

Non-K\"ahler Expanding Ricci Solitons II

We produce new non-Kähler, non-Einstein, complete expanding gradient Ricci solitons with conical asymptotics and underlying manifold of the form R × M2 × · · · × Mr, where r ≥ 2 and Mi are arbitrary

Cohomogeneity one Ricci Solitons from Hopf Fibrations

This paper studies cohomogeneity one Ricci solitons. If the isotropy representation of the principal orbit $G/K$ consists of two inequivalent $Ad_K$-invariant irreducible summands, the existence of

Cohomogeneity One Manifolds of Spin(7) and G2 Holonomy

In this paper, we look for metrics of cohomogeneity one in D = 8 and D = 7 dimensions with Spin(7) and G2 holonomy respectively. In D = 8, we first consider the case of principal orbits that are S 7

Homogeneous nearly Kähler manifolds

We classify six-dimensional homogeneous nearly Kahler manifolds and give a positive answer to Gray and Wolf's conjecture: every homogeneous nearly Kahler manifold is a Riemannian 3-symmetric space

Metrics with exceptional holonomy

It is proved that there exist metrics with holonomy G2 and Spin(7), thus settling the remaining cases in Berger's list of possible holonomy groups. We first reformulate the "holonomy H" condition as

The initial value problem for cohomogeneity one Einstein metrics

The PDE Ric(g) = λ · g for a Riemannian Einstein metric g on a smooth manifold M becomes an ODE if we require g to be invariant under a Lie group G acting properly on M with principal orbits of

A Family of Steady Ricci Solitons and Ricci-flat Metrics

We produce new non-K\"ahler complete steady gradient Ricci solitons whose asymptotics combine those of the Bryant solitons and the Hamilton cigar. We also obtain a family of complete Ricci-flat