Paper · Jul 8, 2019

Yamabe flow on modified Riemann extension

Harish D

math.DGWider flowsarXiv:1907.10391
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Abstract

In this paper the rate relations of Riemann, conformal, conharmonic and Weyl curvature tensors under Yamabe flow are studied. Modified Riemann extensions under Yamabe flow is discussed. The paper ends with remarks on some standard metrics.

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Submitted
Jul 8, 2019
Subjects
math.DG

Comments: 7 pages

Yamabe flow

Its neighbourhood

Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Convergence of the Yamabe flow on manifolds with minimal boundary (Sergio Almaraz and Liming Sun, 2016)4Almaraz 2016 Existence and properties of ancient solutions of the Yamabe flow (Shu-Yu Hsu, 2016)3Hsu 2016 On the Chern-Yamabe flow (Mehdi Lejmi and Ali Maalaoui, 2017)7Lejmi 2017 Convergence of the CR Yamabe Flow (Pak Tung Ho, Weimin Sheng and Kunbo Wang, 2017)1Ho 2017 Infinite-time incompleteness of noncompact Yamabe flow (Jin Takahashi and Hikaru Yamamoto, 2021)6Takahashi 2021 The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant (Gilles Carron, Eric Chen and Yi Wang, 2022)8Carron 2022 Convergence rate of the weighted Yamabe flow (Pak Tung Ho, Jinwoo Shin and Zetian Yan, 2022)2Ho 2022 A non-convergence phenomenon for the CR Yamabe flow (Claudio Afeltra, Andrea Pinamonti and Pak Tung Ho, 2026)5Afeltra 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Convergence of the CR Yamabe Flow

    Pak Tung Ho, Weimin Sheng and Kunbo WangWider flows

    Topics Yamabe flow

  2. Convergence rate of the weighted Yamabe flow

    Pak Tung Ho, Jinwoo Shin and Zetian YanWider flows

    Topics Yamabe flow

  3. Existence and properties of ancient solutions of the Yamabe flow

    Shu-Yu HsuWider flows

    Topics Yamabe flow

  4. Convergence of the Yamabe flow on manifolds with minimal boundary

    Sergio Almaraz and Liming SunWider flows

    Topics Yamabe flow

  5. A non-convergence phenomenon for the CR Yamabe flow

    Claudio Afeltra, Andrea Pinamonti and Pak Tung HoWider flows

    Topics Yamabe flow

  6. Infinite-time incompleteness of noncompact Yamabe flow

    Jin Takahashi and Hikaru YamamotoWider flows

    Topics Yamabe flow

  7. On the Chern-Yamabe flow

    Mehdi Lejmi and Ali MaalaouiWider flows

    Topics Yamabe flow · Shared terms “modified”

  8. The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant

    Gilles Carron, Eric Chen and Yi WangWider flows

    Topics Yamabe flow

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.

Yamabe flow Wider flows The Yamabe flow deforms a metric inside its conformal class at a rate set by scalar curvature. It is a parabolic approach to the Yamabe problem… Start with: The yamabe flow on locally conformally flat manifolds with positive ricci curvature (Chow, 1992)

In the guidebook

  1. 6C.4
    The Yamabe Problem and Critical ExponentsBook 6C · Nonlinear PDE: Variational and Geometric Methods

    Conformal changes of scalar curvature, the Yamabe functional, Aubin's threshold and Schoen's solution, concentration compactness and bubbles, and why Perelman's log-Sobolev minimisers always exist.