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1
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Real hypersurfaces in a nonflat complex space form and their almost contact metric structures

100%
Kim Y., Maeda S.
Colloquium Mathematicum
|
2011
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tom 124
|
nr 1
117-131
EN
We characterize homogeneous real hypersurfaces of types (A₀), (A₁) and (B) in a complex projective space or a complex hyperbolic space.
2
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Circular cone and its Gauss map

81%
Choi M., Kim D.-S., Kim Y., Yoon D.
Colloquium Mathematicum
|
2012
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tom 129
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nr 2
203-210
EN
The family of cones is one of typical models of non-cylindrical ruled surfaces. Among them, the circular cones are unique in the sense that their Gauss map satisfies a partial differential equation similar, though not identical, to one characterizing the so-called 1-type submanifolds. Specifically, for the Gauss map G of a circular cone, one has ΔG = f(G+C), where Δ is the Laplacian operator, f is a non-zero function and C is a constant vector. We prove that circular cones are characterized by being the only non-cylindrical ruled surfaces with ΔG = f(G+C) for a nonzero constant vector C.
3
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Rotation surfaces with L₁-pointwise 1-type Gauss map in pseudo-Galilean space

81%
Yoon D., Kim Y., Jung J.
Annales Polonici Mathematici
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2015
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tom 113
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nr 3
255-267
EN
We study rotation surfaces in the three-dimensional pseudo-Galilean space G₃¹ such that the Gauss map G satisfies the condition L₁G = f(G + C) for a smooth function f and a constant vector C, where L₁ is the Cheng-Yau operator.
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