TY - JOUR
T1 - An Almost Complex Chern–Ricci Flow
AU - Zheng, Tao
N1 - Publisher Copyright:
© 2017, Mathematica Josephina, Inc.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - We consider the evolution of an almost Hermitian metric by the (1, 1) part of its Chern–Ricci form on almost complex manifolds. This is an evolution equation first studied by Chu and coincides with the Chern–Ricci flow if the complex structure is integrable and with the Kähler–Ricci flow if moreover the initial metric is Kähler. We find the maximal existence time for the flow in term of the initial data and also give some convergence results. As an example, we study this flow on the (locally) homogeneous manifolds in more detail.
AB - We consider the evolution of an almost Hermitian metric by the (1, 1) part of its Chern–Ricci form on almost complex manifolds. This is an evolution equation first studied by Chu and coincides with the Chern–Ricci flow if the complex structure is integrable and with the Kähler–Ricci flow if moreover the initial metric is Kähler. We find the maximal existence time for the flow in term of the initial data and also give some convergence results. As an example, we study this flow on the (locally) homogeneous manifolds in more detail.
KW - Almost Hermitian metric
KW - Evolution equation
KW - Maximal time existence
KW - The Chern–Ricci form
UR - http://www.scopus.com/inward/record.url?scp=85023748268&partnerID=8YFLogxK
U2 - 10.1007/s12220-017-9898-9
DO - 10.1007/s12220-017-9898-9
M3 - Article
AN - SCOPUS:85023748268
SN - 1050-6926
VL - 28
SP - 2129
EP - 2165
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 3
ER -