Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces

Gil Solanes

doi:10.1090/S0002-9947-05-03828-6

Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces

Gil Solanes^*

^*Autor corresponent d’aquest treball

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40 Cites (Scopus)

Resum

We give an integral-geometric proof of the Gauss-Bonnet theorem for hypersurfaces in constant curvature spaces. As a tool, we obtain variation formulas in integral geometry with interest in its own.

Idioma original	Anglès
Pàgines (de-a)	1105-1115
Nombre de pàgines	11
Revista	Transactions of the American Mathematical Society
Volum	358
Número	3
DOIs	https://doi.org/10.1090/S0002-9947-05-03828-6
Estat de la publicació	Publicada - de març 2006

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10.1090/S0002-9947-05-03828-6

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title = "Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces",

abstract = "We give an integral-geometric proof of the Gauss-Bonnet theorem for hypersurfaces in constant curvature spaces. As a tool, we obtain variation formulas in integral geometry with interest in its own.",

keywords = "Integral geometry, Total curvature",

author = "Gil Solanes",

year = "2006",

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language = "English",

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AB - We give an integral-geometric proof of the Gauss-Bonnet theorem for hypersurfaces in constant curvature spaces. As a tool, we obtain variation formulas in integral geometry with interest in its own.

KW - Integral geometry

KW - Total curvature

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U2 - 10.1090/S0002-9947-05-03828-6

DO - 10.1090/S0002-9947-05-03828-6

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Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces

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