Valter Borges

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math.DG2025

The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor

Valter Borges, Matheus Andrade Ribeiro de Moura Horácio, João Paulo dos Santos

In this article, we give a new proof of a result due to J. Kim, which states that the Ricci tensor of a gradient Ricci soliton with dimension $n \geq 4$ and harmonic Weyl tensor ha…

math.DG2025

On gradient $ρ$ -Einstein solitons with Bach tensor radially nonnegative

Maria Andrade, Valter Borges, Hiuri Reis

In this paper, we study $n$ -dimensional gradient $ρ$ -Einstein solitons whose Bach tensor is radially nonnegative. Under this assumption, we show that such $ρ$ -Einstein solitons are…

math.DG2023

Topology at infinity of complete gradient Schouten solitons

Valter Borges, Hector Rosero-Garcia, João Paulo dos Santos

In this paper, we study ends of complete gradient non-trivial Schouten solitons. Without any additional assumptions, we show the shrinking ones have finitely many ends, and the exp…

math.DG2023

Ends of shrinking gradient $ρ$ -Einstein solitons

Valter Borges, Hector Rosero-García, João Paulo dos Santos

We prove that all ends of a gradient shrinking $ρ$ -Einstein soliton are $φ$ -non-parabolic, provided $ρ$ is nonnegative and the soliton has bounded and nonnegative scalar curvature,…

The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor

On gradient ρ-Einstein solitons with Bach tensor radially nonnegative

Topology at infinity of complete gradient Schouten solitons

Ends of shrinking gradient ρ-Einstein solitons

On gradient $ρ$ -Einstein solitons with Bach tensor radially nonnegative

Ends of shrinking gradient $ρ$ -Einstein solitons