3 citations · 6 across the 6 of their papers we have counts for
6 papers
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…
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…
Variational problems for integral invariants of the second fundamental form of a map between pseudo-Riemannian manifolds
Rika Akiyama, Takashi Sakai, Yuichiro Sato
We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riema…
Totally umbilical submanifolds in pseudo-Riemannian space forms
Yuichiro Sato
A totally umbilical submanifold in pseudo-Riemannian manifolds is a fundamental notion, which is characterized by the condition that the second fundamental form is proportional to…
-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…
On the classification of ruled minimal surfaces in pseudo-Euclidean space
Yuichiro Sato
This paper gives, in generic situations, a complete classification of ruled minimal surfaces in pseudo-Euclidean space with arbitrary index. In addition, we discuss the condition f…