Holomorphicity of Minimal Submanifolds in Complex Space Forms.
In this paper, we study -dimensional complete connected and oriented space-like hypersurfaces in an (n+1)-dimensional Lorentzian space form with non-zero constant -th mean curvature and two distinct principal curvatures and . We give some characterizations of Riemannian product and show that the Riemannian product is the only complete connected and oriented space-like hypersurface in with constant -th mean curvature and two distinct principal curvatures, if the multiplicities of...
An explicit representation for ideal CR submanifolds of a complex hyperbolic space has been derived in T. Sasahara (2002). We simplify and reformulate the representation in terms of certain Kähler submanifolds. In addition, we investigate the almost contact metric structure of ideal CR submanifolds in a complex hyperbolic space. Moreover, we obtain a codimension reduction theorem for ideal CR submanifolds in a complex projective space.
Dans cet article nous nous intéressons aux immersions isométriques minimales (resp. pluriharmoniques) définies sur une variété riemannienne munie d’une 2-forme parallèle non triviale à valeurs dans une variété riemannienne ou kählérienne de courbure isotrope négative (resp. positive). Les résultats que nous obtenons généralisent certains résultats bien connus de non existence et de rigidité concernant les immersions minimales et pluriharmoniques de variétés kählériennes dans les espaces formes réels...