Yuichiro Sato

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20182025

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math.DG2025

Lorentzian homogeneous Ricci-flat metrics on almost abelian Lie groups

Yuichiro Sato, Takanao Tsuyuki

When the identity component of the full isometry group of a four-dimensional spacetime acts simply transitively, the unique Ricci-flat metric is the Petrov solution. This isometry…

math.DG2018

$d$ -minimal surfaces in three-dimensional singular semi-Euclidean space $R^{0, 2, 1}$

Yuichiro Sato

In this paper, we investigate surfaces in singular semi-Euclidean space $R^{0, 2, 1}$ endowed with a degenerate metric. We define $d$ -minimal surfaces, and give a representa…

Lorentzian homogeneous Ricci-flat metrics on almost abelian Lie groups

d-minimal surfaces in three-dimensional singular semi-Euclidean space R0,2,1

$d$ -minimal surfaces in three-dimensional singular semi-Euclidean space $R^{0, 2, 1}$