3 papers
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…
gr-qc2023
Spatially homogeneous solutions of vacuum Einstein equations in general dimensions
Yuichiro Sato, Takanao Tsuyuki
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological co…
math.DG2018
-minimal surfaces in three-dimensional singular semi-Euclidean space
Yuichiro Sato
In this paper, we investigate surfaces in singular semi-Euclidean space endowed with a degenerate metric. We define -minimal surfaces, and give a representa…