[引用][C] Compact Hopf hypersurfaces of constant mean curvature in complex space forms
V Miquel - Annals of Global Analysis and Geometry, 1994 - Springer
Annals of Global Analysis and Geometry, 1994•Springer
… The purpose of this note is to give a first step to an Alexandrov's like theorem for real
hypersurfaces in a complex space form. In fact, we shall prove that certain Hopf
hypersurfaces (a special case of real hypersurfaces) of constant mean curvature are
geodesic spheres. The restriction to Hopf hypersurfaces is very natural by technical reasons
and has been used in other classification problems of real hypersurfaces of complex space
forms (see [CR], [Ki], [Be1], [Be2] and [KM]). Here, we shall denote by j/(n(A) a …
hypersurfaces in a complex space form. In fact, we shall prove that certain Hopf
hypersurfaces (a special case of real hypersurfaces) of constant mean curvature are
geodesic spheres. The restriction to Hopf hypersurfaces is very natural by technical reasons
and has been used in other classification problems of real hypersurfaces of complex space
forms (see [CR], [Ki], [Be1], [Be2] and [KM]). Here, we shall denote by j/(n(A) a …
Abstract
We prove that every connected compact Hopf hypersurface of a complex space form , contained in a geodesic ball of radius strictly smaller than the injectivity radius of , having constant mean curvature and with if if λ < 0 is a geodesic sphere of .
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