Isometric immersions of warped products
We provide conditions under which an isometric immersion of a (warped) product of manifolds into a space form must be a (warped) product of isometric immersions.
math.DG↗
arXiv subjects
T. Vlachos
Publications and source records attributed to T. Vlachos.
Complete minimal hypersurfaces in the hyperbolic space $\mathbb{H}^4$ with vanishing Gauss-Kronecker curvature
We investigate 3-dimensional complete minimal hypersurfaces in the hyperbolic space $\mathbb{H}^{4}$ with Gauss-Kronecker curvature identically zero. More precisely, we give a classification of complete minimal hypersurfaces with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature bounded from below.
math.DG↗
Complete minimal hypersurfaces of $S^4$ with zero Gauss-Kronecker curvature
We investigate the structure of 3-dimensional complete minimal hypersurfaces in the unit sphere with Gauss-Kronecker curvature identically zero.
math.DG↗
Minimal hypersurfaces with zero Gauss-Kronecker curvature
We investigate complete minimal hypersurfaces in the Euclidean space $% \ {R}^{4}$, with Gauss-Kronecker curvature identically zero. We prove that, if $f:M^{3}\to {R}^{4}$ is a complete minimal hypersurface with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature bounded from below, then $f(M^{3})$ splits as a Euclidean product $L^{2}\times {R}$, where $L^{2}$ is a complete minimal surface in $ {R}^{3}$ with Gaussian curvature bounded from below.
math.DG↗