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

Tasseten, Kezban
Tekin, Bayram
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.
Journal of High Energy Physics
Citation Formats
K. Tasseten and B. Tekin, “A new geometric flow on 3-manifolds: the K-flow,” Journal of High Energy Physics, vol. 2023, no. 10, pp. 0–0, 2023, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/106298.