Total curvature of complete surfaces in hyperbolic space

Gil Solanes

doi:10.1016/j.aim.2010.03.015

Total curvature of complete surfaces in hyperbolic space

Gil Solanes

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Resumen

We prove a Gauss-Bonnet formula for the extrinsic curvature of complete surfaces in hyperbolic space under some assumptions on the asymptotic behavior. The result is given in terms of the measure of geodesics intersecting the surface non-trivially, and of a conformal invariant of the curve at infinity. © 2010 Elsevier Inc.

Idioma original	Inglés
Páginas (desde-hasta)	805-825
Publicación	Advances in Mathematics
Volumen	225
DOI	https://doi.org/10.1016/j.aim.2010.03.015
Estado	Publicada - 1 ene 2010

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title = "Total curvature of complete surfaces in hyperbolic space",

abstract = "We prove a Gauss-Bonnet formula for the extrinsic curvature of complete surfaces in hyperbolic space under some assumptions on the asymptotic behavior. The result is given in terms of the measure of geodesics intersecting the surface non-trivially, and of a conformal invariant of the curve at infinity. {\textcopyright} 2010 Elsevier Inc.",

keywords = "53C65, Hyperbolic space, Integral geometry, Open surfaces, Total curvature",

author = "Gil Solanes",

year = "2010",

month = jan,

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doi = "10.1016/j.aim.2010.03.015",

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N2 - We prove a Gauss-Bonnet formula for the extrinsic curvature of complete surfaces in hyperbolic space under some assumptions on the asymptotic behavior. The result is given in terms of the measure of geodesics intersecting the surface non-trivially, and of a conformal invariant of the curve at infinity. © 2010 Elsevier Inc.

AB - We prove a Gauss-Bonnet formula for the extrinsic curvature of complete surfaces in hyperbolic space under some assumptions on the asymptotic behavior. The result is given in terms of the measure of geodesics intersecting the surface non-trivially, and of a conformal invariant of the curve at infinity. © 2010 Elsevier Inc.

KW - 53C65

KW - Hyperbolic space

KW - Integral geometry

KW - Open surfaces

KW - Total curvature

U2 - 10.1016/j.aim.2010.03.015

DO - 10.1016/j.aim.2010.03.015

M3 - Article

SN - 0001-8708

VL - 225

SP - 805

EP - 825

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Total curvature of complete surfaces in hyperbolic space

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