Horotight spheres in Hyperbolic space
Preprint Series # 932 Buosi, Marcelo and Izumiya, Shyuichi and Maria Aparecida, Soares Ruas Horotight spheres in Hyperbolic space. (14 January 2009); (Submitted) AbstractWe study horotight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horotightness of spheres,
answering a question proposed by T. Cecil and P. Ryan.
For instance, we prove that a sphere is horotight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horotight spheres in hyperbolic space are metric spheres. We also prove that horotight hyperspheres are characterized by the property that
both of its total absolute horospherical curvatures attend their minimum value. We also introduce the notion of weak horotightness: an immersion is weak horotight
if only one of its total absolute curvature attends its minimum.
We prove a characterization theorem for weak horotight hyperspheres.
