Cotton flow

Kisisel A. U. O., Sarioglu O., TEKİN B.

CLASSICAL AND QUANTUM GRAVITY, cilt.25, sa.16, 2008 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 16
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1088/0264-9381/25/16/165019
  • Dergi Adı: CLASSICAL AND QUANTUM GRAVITY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Using the conformally-invariant Cotton tensor, we define a geometric flow, the Cotton flow, which is exclusive to three dimensions. This flow tends to evolve the initial metrics into conformally flat ones, and is somewhat orthogonal to the Yamabe flow, the latter being a flow within a conformal class. We define an entropy functional, and study the flow of nine homogeneous spaces both numerically and analytically. In particular, we show that the arbitrarily deformed homogeneous 3-sphere flows into the round 3-sphere. Two of the nine homogeneous geometries, which are degenerated by the Ricci flow, are left intact by the Cotton flow.