6533b858fe1ef96bd12b6c65
RESEARCH PRODUCT
Immersions of compact riemannian manifolds into a ball of a complex space form
Vicente MiquelFrancisco J. CarrerasFernando Giménezsubject
Pure mathematicsCurvature of Riemannian manifoldsGeneral MathematicsMathematical analysisRiemannian geometryManifoldsymbols.namesakeRicci-flat manifoldsymbolsMathematics::Differential GeometrySectional curvatureExponential map (Riemannian geometry)Ricci curvatureScalar curvatureMathematicsdescription
There are some classical theorems on non-immersibility of compact riemannian manifolds with sectional curvature bounded from above given by Tompkins, O’Neill, Chern, Kuiper and Moore (see [3], pages 221-226). More recently, attention has been paid to the case of immersions into a geodesic ball of a simply connected space form, and some conditions of non-immersibility in such a ball have been proved. In particular, estimates for the mean curvature of a complete immersion into a geodesic ball have been obtained by Jorge and Xavier [11] and a corresponding rigidity theorem for compact hypersurfaces has been proved by Markvorsen [14]. In this paper we give the Kahler analogs of the theorems of Jorge and Xavier (only for the compact case) and Markvorsen, and get some other new results for the Kahler case that have no Riemannian analog. In order to state our results we shall introduce some notation and terminology. Given a real number λ, let us consider the functions
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1997-05-01 | Mathematische Zeitschrift |