The Berger–Ebin theorem and harmonic maps and flows

S. E. Stepanov

Chair of Mathematics, Financial University at the Government of the Russian Federation, Moscow, Russia

Abstract: The goal of this paper is the geometrization of the Berger–Ebin theorem. We use this theorem for studying harmonic maps and flows, in particular, the Ricci solitons. Moreover, we explain the role of a vector field in the corresponding expansions.

Keywords: Berger–Ebin theorem, harmonic maps and flows, infinitesimal harmonic transforms.

UDC: 514.764

Received: 11.04.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:4, 70–74

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