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Heintze–Karcher and Jellett‐type theorems in conformally flat spaces

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  • Paulo Alexandre Sousa
  • Alexandre Bezerra Lima
  • Abdênago Alves de Barros

Abstract

In this paper, we consider a class of conformally flat spaces that includes the space forms as well as the doubled Schwarzschild space, and, we will prove an extension of Jellett's theorem. Next, we build an example, where the extension of Jellett's theorem does not hold. We also prove a Heintze–Karcher‐type inequality and we presented a one‐parametric family of conformally flat spaces, all distinct from space forms, where it holds a Heintze–Karcher‐type inequality.

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  • Paulo Alexandre Sousa & Alexandre Bezerra Lima & Abdênago Alves de Barros, 2023. "Heintze–Karcher and Jellett‐type theorems in conformally flat spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 296(11), pages 5030-5041, November.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:11:p:5030-5041
    DOI: 10.1002/mana.202200218
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