Geodesic
Infinitesimal Harmonic Transformations and Ricci Solitons
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 150-159

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A Ricci soliton on a smooth manifold $M$ is a triple $(g_0,\xi,\lambda)$, where $g_0$ is a complete Riemannian metric, $\xi$ a vector field, and $\lambda$ a constant such that the Ricci tensor $\mathrm{Ric}_0$ of $g_0$ satisfies the equation $-2\mathrm{Ric}_0=L_\xi g_0+2\lambda g_0$. In the paper, we study the geometry of Ricci solitons in dependence of the properties of the vector field $\xi$. In particular, we prove that this vector field is a harmonic transformation.
Keywords: Riemannian manifold, infinitesimal harmonic transformation
Mots-clés : Ricci soliton. 
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     title = {Infinitesimal {Harmonic} {Transformations} and {Ricci} {Solitons}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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S. E. Stepanov; I. G. Shandra; V. N. Shelepova. Infinitesimal Harmonic Transformations and Ricci Solitons. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 150-159. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a11/