\(\phi\)-sectional curvatures of homogeneous real hypersurfaces in a complex projective space. (English) Zbl 1530.53033
This paper addresses the computation of \(\phi\)-sectional curvatures for certain families of homogeneous real hypersurfaces in a complex projective space. Drawing on previous work, the author classifies these hypersurfaces into six types, providing a comprehensive framework for understanding their geometric properties.
The strength of the paper lies in calculating the maximum and minimum values of \(\phi\)-sectional curvatures for homogeneous real hypersurfaces of types (C), (D), and (E) according to his classification.
The strength of the paper lies in calculating the maximum and minimum values of \(\phi\)-sectional curvatures for homogeneous real hypersurfaces of types (C), (D), and (E) according to his classification.
Reviewer: Alcides De Carvalho (Maceió)
MSC:
| 53B25 | Local submanifolds |
| 53A07 | Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces |
| 53C40 | Global submanifolds |
| 53A20 | Projective differential geometry |
References:
| [1] | Cho, J.T., Kimura, M.: Real hypersurfaces with constant\( \phi \)-sectional curvature in complex projective space. Differ. Geom. Appl. 6(8), 101573 (2020) · Zbl 1435.53044 |
| [2] | Kimura, M., Real hypersurfaces and complex submanifolds in complex projective space, Trans. Am. Math. Soc., 296, 137-149 (1986) · Zbl 0597.53021 · doi:10.1090/S0002-9947-1986-0837803-2 |
| [3] | Kimura, M.: Sectional curvatures of holomorphic planes on a real hypersurface in\(P^n({\mathbb{C} })\). Math. Ann. 276, 487-497 (1987) · Zbl 0605.53023 |
| [4] | Kimura, M., Minimal immersions of some circle bundles over holomorphic curves in complex quadric to sphere, Osaka J. Math., 37, 883-903 (2000) · Zbl 1022.53051 |
| [5] | Kimura, M.; Maeda, S.; Tanabe, H., Sectinal curvatures of homogeneous real hypersurfaces of types (A) and (B) in a complex projective space, J. Geom., 112, 23 (2021) · Zbl 1473.53033 · doi:10.1007/s00022-021-00585-4 |
| [6] | Maeda, S., Kimura, M.: Sectional curvatures of some homogeneous real hypersurfaces in a complex projective space. In: Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics, pp. 196-204. World Scientific Publishing, Hackensack (2007) · Zbl 1133.53042 |
| [7] | Maeda, Y., On real hypersurfaces of a complex projective space, J. Math. Soc. Jpn., 28, 529-540 (1976) · Zbl 0324.53039 · doi:10.2969/jmsj/02830529 |
| [8] | Okumura, M., On some real hypersurfaces of a complex projective space, Trans. Am. Math. Soc., 212, 355-364 (1975) · Zbl 0288.53043 · doi:10.1090/S0002-9947-1975-0377787-X |
| [9] | Takagi, R., On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math., 10, 495-506 (1973) · Zbl 0274.53062 |
| [10] | Takagi, R., Real hypersurfaces in a complex projective space with constant principal curvatures, J. Math. Soc. Jpn., 27, 43-53 (1975) · Zbl 0292.53042 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
