Yoshihiko Suyama

Conformally flat hypersurfaces with cyclic guichard net

We classify the 3-dimensional conformally flat hypersurfaces with cyclic principal Guichard net. The orthogonal surfaces of the cyclic system turn out to be linear Weingarten surfaces in suitable ambient space forms and we provide explicit parametrizations for the conformally flat hypersurfaces.

CONFORMALLY FLAT HYPERSURFACES WITH BIANCHI-TYPE GUICHARD NET

We obtain a partial classification result for generic

Curvilinear coordinates on generic conformally flat hypersurfaces and constant curvature 2-metrics

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Ribaucour Pairs Corresponding to Dual Pairs of Conformally Flat Hypersurfaces

-dimensional conformally flat hypersurfaces in the conformal

A CLASSIFICATION AND A NON-EXISTENCE THEOREM FOR CONFORMALLY FLAT HYPERSURFACES IN EUCLIDEAN 4-SPACE

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Conformally flat hypersurfaces in Euclidean 4-space II

-sphere: explicit analytic data are obtained for conformally flat hypersurfaces with Bianchi-type canonical Guichard net. This is the first classification result for conformally flat hypersurfaces without additional symmetry. We discuss the curved flat associated family for conformally flat hypersurfaces and show that it descends to an associated family of conformally flat hypersurfaces. The associated family of conformally flat hypersurfaces with Bianchi-type Guichard net is investigated.

Differentiable sphere theorem by curvature pinching

There is a one-to-one correspondence between associated families of generic conformally flat (local-)hypersurfaces in 4-dimensional space forms and conformally flat 3-metrics with the Guichard condition. In this paper, we study the space of conformally flat 3-metrics with the Guichard condition: for a conformally flat 3-metric with the Guichard condition in the interior of the space, an evolution of orthogonal (local-) Riemannian

A duality for conformally flat hypersurfaces

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Explicit representation of compact conformally flat hypersurfaces

-metrics with constant Gauss curvature

A differentiable sphere theorem by curvature pinching II

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