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arXiv · 2512.09653

Observações sobre funções potenciais de variedades quase-Einstein não compactas

Jaciane Gönçalves
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Abstract

Neste artigo, estudamos o conjunto de funções potenciais em variedades quase Einstein não compactas. Mostramos que o espaço de todas as funções potenciais positivas em uma variedade tridimensional não compacta quase-Einstein tem dimensão no máximo dois, e que a igualdade vale se e somente se a variedade for isométrica a um produto $B\times\mathbb{R}$, onde $B$ é uma superfície $λ$-Einstein ou um dos exemplos obtidos por L. Berard Bergery e descritos no livro de Besse. Além disso, provamos que qualquer variedade quase-Einstein assintoticamente plana $n$-dimensional com $λ=0$ é necessariamente Ricci-plana.

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Jaciane Gönçalves. 2026-09-18. Observações sobre funções potenciais de variedades quase-Einstein não compactas. https://arxiv.org/abs/2512.09653

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