Real Hypersurfaces of Complex Projective Spaces.
On Real Hypersurfaces of a Complex Projective Space.
Imbedding of a Complex Projective Space Defined by Monomials of Same Degree.
Isoparametric hypersurfaces with less than four principal curvatures in a sphere
We characterize Clifford hypersurfaces and Cartan minimal hypersurfaces in a sphere by some properties of extrinsic shapes of their geodesics.
A Useful Characterization of Some Real Hypersurfaces in a Nonflat Complex Space Form
We characterize totally η-umbilic real hypersurfaces in a nonflat complex space form M̃ₙ(c) (= ℂPⁿ(c) or ℂHⁿ(c)) and a real hypersurface of type (A₂) of radius π/(2√c) in ℂPⁿ(c) by observing the shape of some geodesics on those real hypersurfaces as curves in the ambient manifolds (Theorems 1 and 2).
Shape Operators and Structure Tensors of Real Hypersurfaces in Nonflat Quaternionic Space Forms
We characterize curvature-adapted real hypersurfaces in nonflat quaternionic space forms in terms of their shape operators and structure tensors.
Characterization of totally umbilic hypersurfaces in a space form by circles
In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.
Lie derivatives on real hypersurfaces in a complex projective space
Real hypersurfaces in a nonflat complex space form and their almost contact metric structures
We characterize homogeneous real hypersurfaces of types (A₀), (A₁) and (B) in a complex projective space or a complex hyperbolic space.
Geometry of holomorphic distributions of real hypersurfaces in a complex projective space
We characterize homogeneous real hypersurfaces ’s of type , and of a complex projective space in the class of real hypersurfaces by studying the holomorphic distribution of .
A characterization of a certain real hypersurface of type in a complex projective space
In the class of real hypersurfaces isometrically immersed into a nonflat complex space form of constant holomorphic sectional curvature which is either a complex projective space or a complex hyperbolic space according as or , there are two typical examples. One is the class of all real hypersurfaces of type (A) and the other is the class of all ruled real hypersurfaces. Note that the former example are Hopf manifolds and the latter are non-Hopf manifolds. In this...
Geometric properties of Lie hypersurfaces in a complex hyperbolic space
We study homogeneous real hypersurfaces having no focal submanifolds in a complex hyperbolic space. They are called Lie hypersurfaces in this space. We clarify the geometry of Lie hypersurfaces in terms of their sectional curvatures, the behavior of the characteristic vector field and their holomorphic distributions.
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