Yuichiro Sato

Yuichiro Sato
  • PhD in Mathematics
  • Assistant Professor at Waseda University

About

4
Publications
728
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15
Citations
Introduction
Skills and Expertise
Differential Geometry
Riemannian Geometry
Pseudo-Riemannian Geometry
Submanifold theory
Current institution
Waseda University
Waseda University
  • Global Education Center
  • Tokyo, Japan
Current position
  • Assistant Professor

Publications

Publications (4)
Figure 1: Upper-left: the minimal hyperbolic paraboloid. Upper-right:...
Figure 2: (a) Upper-left: (F, G) = (w, 1 w ). (b) Upper-right: (F, G) =...
d−MinimalSurfacesinThree−DimensionalSingularSemi−EuclideanSpace-Minimal Surfaces in Three-Dimensional Singular Semi-Euclidean Space \mathbb{R}^{0,2,1}
Article
Full-text available
  • Jan 2021
In this paper, we investigate surfaces in singular semi-Euclidean space $\mathbb{R}^{0,2,1}$ endowed with a degenerate metric. We define $d$-minimal surfaces, and give a representation formula of Weierstrass type. Moreover, we prove that $d$-minimal surfaces in $\mathbb{R}^{0,2,1}$ and spacelike flat zero mean curvature (ZMC) surfaces in four-dimen...
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Totally umbilical submanifolds in pseudo-Riemannian space forms
Preprint
Full-text available
  • May 2020
A totally umbilical submanifold in pseudo-Riemannian manifolds is a fundamental notion, which is characterized by the fact that the second fundamental form to be proportional to the metric. And, it is also a generalization of a notion of a totally geodesic submanifold. In this paper, we classify congruent classes of full totally umbilical submanifo...
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Figure 1. Elliptic helicoid of the second kind.
Figure 2. Minimal hyperbolic paraboloid.
Figure 3. d-minimal rotational surface.
Figure 4. (F, G) = (z, 1). Figure 5. (F, G) = (z 2 , 1).
+2 Figure 6. (F, G) = (z 3 , 1).
d-minimal surfaces in three-dimensional singular semi-Euclidean space R0,2,1\mathbb{R}^{0,2,1}
Preprint
Full-text available
  • Sep 2018
In this paper, we investigate surfaces in singular semi-Euclidean space $\mathbb{R}^{0,2,1}$ endowed with a degenerate metric. We define $d$-minimal surfaces, and give a representation formula of Weierstrass type. Moreover, we prove that $d$-minimal surfaces in $\mathbb{R}^{0,2,1}$ and spacelike flat zero mean curvature (ZMC) surfaces in four-dimen...
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On the classification of ruled minimal surfaces in pseudo-Euclidean space
Article
Full-text available
  • May 2017
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 for ruled minimal surfaces to exist, and give a counter-example on the problem of Bernstein type.
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