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Réalisations de surfaces hyperboliques complètes dans H 3

Jean-Marc Schlenker (1998)

Annales de l'institut Fourier

Soit K 0 ∈ ] - 1 , 0 [ ; chaque métrique complète à courbure K 0 sur la sphère à N ≥ 1 trous admet une unique réalisation comme métrique induite sur une surface plongée dans H 3 dont le bord à l’infini est une réunion disjointe de cercles. De manière duale, chaque métrique complète à courbure K ˜ 0 ∈ ] - ∞ , 0 [ sans géodésique fermée de longueur L ≤ 2 π se réalise de manière unique comme troisième forme fondamentale d’une surface plongée dont le bord à l’infini est une réunion de cercles.

Revisiting linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space

Weiller F. C. Barboza, H. F. de Lima, M. A. Velásquez (2023)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we deal with n -dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field and flat normal bundle in a locally symmetric semi-Riemannian space L p n + p of index p > 1 , which obeys some curvature constraints (such an ambient space can be regarded as an extension of a semi-Riemannian space form). Under appropriate hypothesis, we are able to prove that such a spacelike submanifold is either totally umbilical or isometric to an isoparametric...

Ricci curvature of real hypersurfaces in complex hyperbolic space

Bang-Yen Chen (2002)

Archivum Mathematicum

First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.

Rigidity of Rank-One Factors of Compact Symmetric Spaces

Andrew Clarke (2011)

Annales de l’institut Fourier

We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.

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