Revisiting Liebmann’s theorem in higher codimension

• Autorzy: Araújo Jogli G. , Lima Henrique F. de

Identyfikatory

DOI

10.4064/ba190514-30-5

• Języki publikacji: EN

Abstrakty

EN

We deal with compact surfaces immersed with flat normal bundle and parallel normalized mean curvature vector field in a space form Q_c^2+p of constant sectional curvature c ϵ {−1, 0, 1}. Such a surface is called an LW-surface when it satisfies a linear Weingarten condition of the type K = aH + b for some real constants a and b, where H and K denote the mean and Gaussian curvatures, respectively. In this setting, we extend the classical rigidity theorem of Liebmann (1899) showing that a non-flat LW-surface with non-negative Gaussian curvature must be isometric to a totally umbilical round sphere.

Słowa kluczowe

EN

space forms; compact LW-surfaces; parallel normalized mean curvature vector field; totally umbilical round spheres

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2019
• Tom: Vol. 67, no. 2
• Strony: 179--185
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Araújo Jogli G.

• Departamento de Matemática, Universidade Federal Rural de Pernambuco, 52.171-900 Recife, Pernambuco, Brazil

autor

Lima Henrique F. de

• Departamento de Matemática, Universidade Federal de Campina Grande, 58.429-970 Campina Grande, Paraíba, Brazil

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).