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Dergiler / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 2

Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving δ(2)

TORU SASAHARA
Sayfa
305–312
Yayın Tarihi
2022-10-18
DOI
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We describe how to obtain all such hypersurfaces.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:It was proved in Chen’s paper (Arch.
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Temel Bulgular & Veri:Math. (Basel) 67 (1996), 519–528) that every real hypersurface in the complex projective plane of constant holomorphic sectional curvature 4 satisfies δ(2) ≤ 9 4 H2 + 5, where H is the mean curvature and δ(2) is a δ-invariant introduced by him.
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Sonuç & Katkı:We describe how to obtain all such hypersurfaces.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

It was proved in Chen’s paper (Arch. Math. (Basel) 67 (1996), 519–528) that every real hypersurface in the complex projective plane of constant holomorphic sectional curvature 4 satisfies δ(2) ≤ 9 4 H2 + 5, where H is the mean curvature and δ(2) is a δ-invariant introduced by him. In this paper, we study non-Hopf real hypersurfaces satisfying the equality case of the inequality under the condition that the mean curvature is constant along each integral curve of the Reeb vector field. We describe how to obtain all such hypersurfaces.

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Bu Makaleye Atıf Yap

SASAHARA, T. (2022). Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving δ(2). International Electronic Journal of Geometry, Cilt: 14 - Sayı: 2, 305–312. https://ajindex.com/articles/539579

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Kaynakça (7)

  1. Cecil, T. E., Ryan, P. J.: Geometry of Hypersurfaces. Springer Monographs in Mathematics. Springer, New York (2015)
  2. Chen, B. Y.: Some pinching and classification theorems for minimal submanifolds. Arch. Math. (Basel) 60, 568-578 (1993)
  3. Chen, B. Y.: A general inequality for submanifolds in complex space forms and its applications. Arch. Math. (Basel) 67, 519–528 (1996)
  4. Chen, B. Y.: Pseudo Riemannian Geometry, δ-invariants and Applications. World Scientific, Hackensack, New Jersey (2011)
  5. Ivey, T. A., Ryan, P. J.: Hypersurfaces in CP 2 and CH2 with two distinct principal curvatures. Glasgow Math. J. 58, 137-152 (2016)
  6. Kimura, M.: Sectional curvatures of holomorphic planes on a real hypersurface in P n(C). Math. Ann. 276, 487–497 (1987)
  7. Sasahara, T.: Real hypersurfaces in the complex projective plane attaining equality in a basic inequality. Houston J. Math. 43, 89-94 (2017)