A new geometric flow on 3-manifolds: the K-flow

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Tasseten K., TEKİN B.

Journal of High Energy Physics, vol.2023, no.10, 2023 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 2023 Issue: 10
  • Publication Date: 2023
  • Doi Number: 10.1007/jhep10(2023)114
  • Journal Name: Journal of High Energy Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH, Directory of Open Access Journals
  • Keywords: Classical Theories of Gravity, Models of Quantum Gravity
  • Middle East Technical University Affiliated: Yes

Abstract

We define a new geometric flow, which we shall call the K-flow, on 3-dimensional Riemannian manifolds; and study the behavior of Thurston’s model geometries under this flow both analytically and numerically. As an example, we show that an initially arbitrarily deformed homogeneous 3-sphere flows into a round 3-sphere and shrinks to a point in the unnormalized flow; or stays as a round 3-sphere in the volume normalized flow. The K-flow equation arises as the gradient flow of a specific purely quadratic action functional that has appeared as the quadratic part of New Massive Gravity in physics; and a decade earlier in the mathematics literature, as a new variational characterization of three-dimensional space forms. We show the short-time existence of the K-flow using a DeTurck-type argument.