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Kähler–Ricci solitons
induced by infinite-dimensional complex space forms
Andrea Loi, Filippo Salis and Fabio Zuddas |
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Vol. 316 (2022), No. 1, 183–205
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Abstract |
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We exhibit families of nontrivial (i.e., not Kähler–Einstein) radial Kähler–Ricci solitons (KRS), both complete and not complete, which can be Kähler immersed into infinite-dimensional complex space forms. This shows that the triviality of a KRS induced by a finite-dimensional complex space form proved by Loi and Mossa (Proc. Amer. Math. Soc. 149:11 (2020), 4931–4941) 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 nonelliptic complex space form is necessarily defined at the origin. |
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Keywords
Kähler metric, Kähler–Ricci solitons, Einstein metrics,
Calabi's diastasis function, complex space forms
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Mathematical Subject Classification
Primary: 32Q15, 53C55
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Milestones
Received: 23 July 2021
Accepted: 27 November 2021
Published: 26 February 2022
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Authors |
| Andrea Loi | |
| Dipartimento di Matematica Università di Cagliari Cagliari Italy |
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| Filippo Salis | |
| Dipartimento di Scienze
Matematiche Politecnico di Torino Torino Italy |
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| Fabio Zuddas | |
| Dipartimento di Matematica Università di Cagliari Cagliari Italy |
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