Compact Surfaces with Constant Gaussian Curvature in Product Spaces
2010 - J.A. Aledo, V. Lozano, J.A. Pastor
Mediterranean Journal of Mathematics 7 (2010), 263-270.
Abtract
We prove that the only compact surfaces of positive constant Gaussian curvature in ?2×? (resp. positive constant Gaussian curvature greater than 1 in ????2×?) whose boundary ? is contained in a slice of the ambient space and such that the surface intersects this slice at a constant angle along ?, are the pieces of a rotational complete surface. We also obtain some area estimates for surfaces of positive constant Gaussian curvature in ?2×? and positive constant Gaussian curvature greater than 1 in ????2×? whose boundary is contained in a slice of the ambient space. These estimates are optimal in the sense that if the bounds are attained, the surface is again a piece of a rotational complete surface.