Second order geometric flows on foliated manifolds

Abstract

We prove a general result about the short time existence and uniqueness of second order geometric flows transverse to a Riemannian foliation on a compact manifold. Our result includes some flows already existing in literature, as the transverse Ricci flow, the Sasaki-Ricci flow and the Sasaki J-flow and motivates the study of other evolution equations. We also introduce a transverse version of the Kaehler-Ricci flow adapting some classical results to the foliated case.

22 pages. Comments are wellcome

References in corpus (1)

• On the J-flow in Sasakian manifolds

Cited by in corpus (4)

• The transverse Chern-Ricci flow
• Transverse Kähler-Ricci flow and deformations of the metric on the Sasaki space $T^{1,1}$
• The Partial Ricci Flow on $\mathfrak{g}$-foliations
• On the convergence of the Sasaki J-flow