arXiv subjects

Reiko Aiyama

Publications and source records attributed to Reiko Aiyama.

3 recordsLinked to original sources

arXiv2016

Remarks on the Gauss images of complete minimal surfaces in Euclidean four-space

We perform a systematic study of the image of the Gauss map for complete minimal surfaces in Euclidean four-space. In particular, we give a geometric interpretation of the maximal number of exceptional values of the Gauss map of a complete orientable minimal surface in Euclidean four-space. We also provide optimal results for the maximal number of exceptional values of the Gauss map of a complete minimal Lagrangian surface in the complex two-space and the generalized Gauss map of a complete nonorientable minimal surface in Euclidean four-space.

math.DG↗

arXiv2015

The Gauss map and total curvature of complete minimal Lagrangian surfaces in the complex two-space

The purpose of this paper is to reveal the relationship between the total curvature and the global behavior of the Gauss map of a complete minimal Lagrangian surface in the complex two-space. To achieve this purpose, we show the precise maximal number of exceptional values of the Gauss map for a complete minimal Lagrangian surface with finite total curvature in the complex two-space. Moreover, we prove that if the Gauss map of a complete minimal Lagrangian surface which is not a Lagrangian plane omits three values, then it takes all other values infinitely many times.

math.DG↗

arXiv2011

3-Manifolds with Positive Flat Conformal Structure

In this paper, we consider a closed 3-manifold $M$ with flat conformal structure $C$. We will prove that, if the Yamabe constant of $(M, C)$ is positive, then $(M, C)$ is Kleinian.

math.DG↗