Compact Conformally Symmetric Riemannan Spaces.
A fundamental question about hypersurfaces in the Euclidean space is to decide if the sphere is the only compact hypersurface (embedded or immersed) with constant higher order mean curvature Hr, for some r = 1, ..., n.
In the present paper we classify all surfaces in 3 with a canonical principal direction. Examples of this type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space 3 is the catenoid.
In this paper, by using Cheng-Yau’s self-adjoint operator , we study the complete hypersurfaces in a sphere with constant scalar curvature.
We show that there exists a complete minimal surface immersed into which is conformally equivalent to a compact hyperelliptic Riemann surface of genus three minus one point. The end of the surface is of Enneper type and its total curvature is .
In this paper we review some topics on the theory of complete minimal surfaces in three dimensional Euclidean space.
In this paper we construct complete minimal surfaces of arbitrary genus in with one, two, three and four ends respectively. Furthermore the surfaces lie between two parallel planes of .
In this paperwe give new existence results for complete non-orientable minimal surfaces in ℝ3 with prescribed topology and asymptotic behavior
In this note we show that any complete Kähler (immersed) Euclidean hypersurface must be the product of a surface in with an Euclidean factor .