caa a22 4500 445883944 CHVBK 20180317145553.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s10711-010-9565-9 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9565-9 Horo-tight spheres in hyperbolic space [Elektronische Daten] [Marcelo Buosi, Shyuichi Izumiya, Maria Ruas] We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by Cecil and Ryan. For instance, we prove that a sphere is horo-tight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horo-tight spheres in hyperbolic space are metric spheres. We also prove that horo-tight 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 horo-tightness: an immersion is weak horo-tight if only one of its total absolute curvature attends its minimum. We prove a characterization theorem for weak horo-tight hyperspheres. Springer Science+Business Media B.V., 2011 Horo-tight immersion nationallicence Sphere nationallicence Hyperbolic space nationallicence Horospherical geometry nationallicence Totally absolute horospherical curvature nationallicence Buosi Marcelo Universidade Federal dos Vales do Jequitinhonha e Mucuri, Rua da Glória 187, 39100-000, Diamantina, MG, Brazil aut Izumiya Shyuichi Department of Mathematics, Hokkaido University, 060-0810, Sapporo, Japan aut Ruas Maria Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil aut Geometriae Dedicata Springer Netherlands 154/1(2011-10-01), 9-26 0046-5755 154:1<9 2011 154 10711 https://doi.org/10.1007/s10711-010-9565-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9565-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Buosi Marcelo Universidade Federal dos Vales do Jequitinhonha e Mucuri, Rua da Glória 187, 39100-000, Diamantina, MG, Brazil aut NATIONALLICENCE 700 1- Izumiya Shyuichi Department of Mathematics, Hokkaido University, 060-0810, Sapporo, Japan aut NATIONALLICENCE 700 1- Ruas Maria Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 154/1(2011-10-01), 9-26 0046-5755 154:1<9 2011 154 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer