Paper · Oct 12, 2016

Invariant Solutions of the Yamabe equation on the Koiso-Cao Soliton

Jonatán Torres Orozco

math.DGarXiv:1610.03891
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Abstract

We consider the non-trivial Ricci soliton on constructed by Koiso and Cao. It is a Kähler metric invariant by the action on . We study its Yamabe equation and prove it has exactly one invariant solution up to homothecies.

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Submitted
Oct 12, 2016
Subjects
math.DG

Comments: 17 pages, 1 figure

Ricci solitonsKähler geometry

Its neighbourhood

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  1. Equivariant solutions to the optimal partition problem for the prescribed Q-curvature equation

    Juan Carlos Fernández, Oscar Palmas and Jonatán Torres Orozco

    Topics Ricci solitons · Same author Jonatán Torres Orozco · Shared terms “Koiso Cao”, “Yamabe”

  2. Ricci solitons

    Andrzej Derdzinski

    Topics Kähler geometry, Ricci solitons · Shared terms “Koiso”, “Cao”

  3. Steady conformally Kähler Ricci solitons with isoparametric potential

    Ernani Ribeiro and Hung Tran

    Topics Kähler geometry, Ricci solitons · Shared terms “Cao solitons”

  4. A family of Kähler flying wing steady Ricci solitons

    Pak-Yeung Chan, Ronan J. Conlon and Yi Lai

    Topics Kähler geometry, Ricci solitons · Shared terms “Cao”

  5. Existence and uniqueness of -invariant Kähler-Ricci solitons

    Johannes Schäfer

    Topics Kähler geometry, Ricci solitons

  6. Hamiltonian -forms and new explicit Calabi–Yau metrics and gradient steady Kähler–Ricci solitons on

    Vestislav Apostolov and Charles Cifarelli

    Topics Kähler geometry, Ricci solitons · Shared terms “Cao”

  7. Nature of Some Solitons on Almost coKähler Manifolds and Asymptotically Harmonic Manifolds

    Paritosh Ghosh, Hemangi Madhusudan Shah and Arindam Bhattacharyya

    Topics Kähler geometry, Ricci solitons · Shared terms “trivial Ricci”

  8. Coupled Kähler-Ricci solitons on toric Fano manifolds

    Jakob Hultgren

    Topics Kähler geometry, Ricci solitons · Shared terms “invariant solutions”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci solitons Metrics that change under Ricci flow only by scaling and diffeomorphisms: shrinking, steady or expanding solitons. Start with: The Ricci flow on surfaces (Hamilton, 1988) Kähler geometry Complex manifolds with compatible Riemannian metrics whose Kähler form is closed. Here Ricci curvature is the complex Hessian of a log-determinant… Start with: On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I (Yau, 1978)

In the guidebook

  1. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

    Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

  2. 12B.2
    The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery

    Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.