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Geometric and analytic results for Einstein solitons

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  • Enrique F. L. Agila
  • José N. V. Gomes

Abstract

We compute a lower bound for the scalar curvature of a gradient Einstein soliton under a certain assumption on its potential function. We establish an asymptotic behavior of the potential function on a noncompact gradient shrinking Einstein soliton. As a result, we obtain the finiteness of its fundamental group and its weighted volume. We also prove some geometric and analytic results for constructing gradient Einstein solitons that are realized as warped metrics, and we give a few explicit examples.

Suggested Citation

  • Enrique F. L. Agila & José N. V. Gomes, 2024. "Geometric and analytic results for Einstein solitons," Mathematische Nachrichten, Wiley Blackwell, vol. 297(8), pages 2855-2872, August.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:8:p:2855-2872
    DOI: 10.1002/mana.202200340
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