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

Creative Commons License

Tasseten K., TEKİN B.

Journal of High Energy Physics, cilt.2023, sa.10, 2023 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2023 Sayı: 10
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/jhep10(2023)114
  • Dergi Adı: Journal of High Energy Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: Classical Theories of Gravity, Models of Quantum Gravity
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.