Abstract
This paper is devoted to Ricci flow on contact manifolds. We define the contact curvature flow and establish a short time existence. Meanwhile, we study a contact Ricci soliton and prove that every solution of the unnormalized contact curvature flow is a selfsimilar solution corresponding to a contact Ricci soliton which is a steady soliton. Finally we show that a time dependent family of contact Einstein, Sasakian, K-contact, or η-Einstein 1-forms η t is a solution of the normalized contact curvature flow if it is a conformal variation of an initial 1-form η 0.
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Original Russian Text Copyright © 2015 Pirhadi V. and Razavi A.
Tehran. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 5, pp. 1142–1153, September–October, 2015; DOI: 10.17377/smzh.2015.56.513.
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Pirhadi, V., Razavi, A. Ricci flow on contact manifolds. Sib Math J 56, 912–921 (2015). https://doi.org/10.1134/S0037446615050134
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DOI: https://doi.org/10.1134/S0037446615050134