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June 2018 Characterizations of three homogeneous real hypersurfaces in a complex projective space
Makoto KIMURA, Sadahiro MAEDA
Hokkaido Math. J. 47(2): 291-316 (June 2018). DOI: 10.14492/hokmj/1529308820

Abstract

In an $n$-dimensional complex hyperbolic space $\mathbb{C}H^n(c)$ of constant holomorphic sectional curvature $c (\lt 0)$, the horosphere HS, which is defined by ${\rm HS} = \lim_{r\to\infty}G(r)$, is one of nice examples in the class of real hypersurfaces. Here, $G(r)$ is a geodesic sphere of radius $r$ $(0 \lt r \lt \infty)$ in $\mathbb{C}H^n(c)$. The second author ([14]) gave a geometric characterization of HS. In this paper, motivated by this result, we study real hypersurfaces $M^{2n-1}$ isometrically immersed into an $n$-dimensional complex projective space $\mathbb{C}P^n(c)$ of constant holomorphic sectional curvature $c(\gt 0)$.

Citation

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Makoto KIMURA. Sadahiro MAEDA. "Characterizations of three homogeneous real hypersurfaces in a complex projective space." Hokkaido Math. J. 47 (2) 291 - 316, June 2018. https://doi.org/10.14492/hokmj/1529308820

Information

Published: June 2018
First available in Project Euclid: 18 June 2018

zbMATH: 06901707
MathSciNet: MR3815294
Digital Object Identifier: 10.14492/hokmj/1529308820

Subjects:
Primary: 53B25
Secondary: 53C40

Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

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Vol.47 • No. 2 • June 2018
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