Kaehler Ricci solitons induced by infinite dimensional complex space forms

Abstract

We exhibit families of non trivial (i.e. not Kaehler-Einstein) radial Kaehler-Ricci solitons (KRS), both complete and not complete, which can be Kaehler immersed into infinite dimensional complex space forms. This result shows that the triviality of a KRS induced by a finite dimensional complex space form proved in [12] does not hold when the ambient space is allowed to be infinite dimensional. Moreover, we show that the radial potential of a radial KRS induced by a non-elliptic complex space form is necessarily defined at the origin.

22 pages

Cited by in corpus (4)

• Holomorphic isometries into homogeneous bounded domains
• On holomorphic isometries into blow-ups of ${\mathbb{C}}^n$
• Rigidity properties of holomorphic isometries into homogeneous Kähler manifolds
• Toric para-Kaehler-Einstein manifolds immersed in para-Kaehler space forms