naa a22 4500 510810780 CHVBK 20180411083441.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s12220-012-9311-7 doi (NATIONALLICENCE)springer-10.1007/s12220-012-9311-7 He Weiyong Department of Mathematics, University of Oregon, 97403, Eugene, OR, USA aut The Sasaki-Ricci Flow and Compact Sasaki Manifolds of Positive Transverse Holomorphic Bisectional Curvature [Elektronische Daten] [Weiyong He] We show that Perelman's ${\mathcal{W}}$ functional on Kähler manifolds has a natural counterpart on Sasaki manifolds. We prove, using this functional, that Perelman's results on Kähler-Ricci flow (the first Chern class is positive) can be generalized to Sasaki-Ricci flow, including the uniform bound on the diameter and the scalar curvature along the flow. We also show that positivity of transverse bisectional curvature is preserved along Sasaki-Ricci flow, using Bando and Mok's methods and results in Kähler-Ricci flow. In particular, we show that the Sasaki-Ricci flow converges to a Sasaki-Ricci soliton when the initial metric has nonnegative transverse bisectional curvature. Mathematica Josephina, Inc., 2012 Sasaki manifolds nationallicence Sasaki-Ricci flow nationallicence Positive transverse bisectional curvature nationallicence Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1876-1931 1050-6926 23:4<1876 2013 23 12220 https://doi.org/10.1007/s12220-012-9311-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-012-9311-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- He Weiyong Department of Mathematics, University of Oregon, 97403, Eugene, OR, USA aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1876-1931 1050-6926 23:4<1876 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer