A new proof of Liebmann classical rigidity theorem for surfaces in space forms

DOI10.1216/rmjm/1181069618zbMath1100.53003OpenAlexW2026846957MaRDI QIDQ2495308

Luis J. Alías, Alfonso Romero, Juan A. Aledo

Publication date: 5 July 2006

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181069618

zbMATH Keywords

sphereGaussian curvaturerigidity theorem

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Non-Euclidean differential geometry (53A35) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45)

Related Items (13)

Cauchy spinors on 3-manifolds ⋮ Spacelike surfaces with positive definite second fundamental form in 3D spacetimes ⋮ Gap theorems for linear Weingarten surfaces ⋮ Willmore surfaces and Hopf tori in homogeneous 3-manifolds ⋮ Closed surfaces with different shapes that are indistinguishable by the SRNF ⋮ Some characterizations of totally umbilical surfaces in three-dimensional warped product spaces ⋮ A Liebmann type theorem for linear Weingarten surfaces ⋮ New characterizations of compact totally umbilical spacelike surfaces in 4-dimensional Lorentz-Minkowski spacetime through a lightcone ⋮ LW-surfaces with higher codimension and Liebmann's theorem in the hyperbolic space ⋮ On the Gauss mapping of hypersurfaces with constant scalar curvature in \(\mathbb H^{n+1}\) ⋮ Revisiting Liebmann’s theorem in higher codimension ⋮ Rigidity of surfaces with constant extrinsic curvature in Riemannian product spaces ⋮ On non-degenerate null normal sections of codimension two spacelike surfaces

Cites Work

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• Compact hypersurfaces with constant scalar curvature and a congruence theorem
• Compact hypersurfaces with constant higher order mean curvatures
• Hypersurfaces with constant inner curvature of the second fundamental form, and the non-rigidity of the sphere
• Zur affinen Differentialgeometrie im Großen. I
• Some new characterizations of the Euclidean sphere
• Characterizations of the Sphere by the Curvature of the Second Fundamental Form
• Two Characteristic Properties of the Sphere
• Closed Convex Hypersurfaces with Second Fundamental Form of Constant Curvature

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