Complete Minimal Spheres and Projective Planes in Rn with Simple Ends.
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 .
Let Mⁿ (n ≥ 3) be an n-dimensional complete super stable minimal submanifold in with flat normal bundle. We prove that if the second fundamental form A of M satisfies , where α ∈ [2(1 - √(2/n)), 2(1 + √(2/n))], then M is an affine n-dimensional plane. In particular, if n ≤ 8 and , d = 1,3, then M is an affine n-dimensional plane. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite -norm curvature in ℝ⁷ are considered.
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 .
We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures with constant scalar curvature is either Einstein, or the dual field of is Killing. Next, let be a complete and connected Riemannian manifold of dimension at least admitting a pair of Einstein-Weyl structures . Then the Einstein-Weyl vector field (dual to the -form ) generates an infinitesimal harmonic transformation if and only if is Killing.
In this paper, we characterize the -dimensional complete spacelike hypersurfaces in a de Sitter space with constant scalar curvature and with two distinct principal curvatures one of which is simple.We show that is a locus of moving -dimensional submanifold , along the principal curvature of multiplicity is constant and is umbilical in and is contained in an -dimensional sphere and is of constant curvature ,where is the arc length of an orthogonal trajectory of the family...