Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 14 Sayı: 2, 305 - 312, 29.10.2021
https://doi.org/10.36890/iejg.936026

Öz

Kaynakça

  • [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 CP2 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 Pn(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).

Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$

Yıl 2021, Cilt: 14 Sayı: 2, 305 - 312, 29.10.2021
https://doi.org/10.36890/iejg.936026

Öz

It was proved in Chen's paper [3] that every real hypersurface in the complex projective plane of constant holomorphic sectional curvature $4$ satisfies $$\delta(2)\leq \frac{9}{4}H^2+5,$$ where $H$ is the mean curvature and $\delta(2)$ is a $\delta$-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.

Kaynakça

  • [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 CP2 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 Pn(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).
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

T. Sasahara 0000-0003-2853-0268

Yayımlanma Tarihi 29 Ekim 2021
Kabul Tarihi 8 Ekim 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 14 Sayı: 2

Kaynak Göster

APA Sasahara, T. (2021). Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$. International Electronic Journal of Geometry, 14(2), 305-312. https://doi.org/10.36890/iejg.936026
AMA Sasahara T. Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$. Int. Electron. J. Geom. Ekim 2021;14(2):305-312. doi:10.36890/iejg.936026
Chicago Sasahara, T. “Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$”. International Electronic Journal of Geometry 14, sy. 2 (Ekim 2021): 305-12. https://doi.org/10.36890/iejg.936026.
EndNote Sasahara T (01 Ekim 2021) Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$. International Electronic Journal of Geometry 14 2 305–312.
IEEE T. Sasahara, “Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$”, Int. Electron. J. Geom., c. 14, sy. 2, ss. 305–312, 2021, doi: 10.36890/iejg.936026.
ISNAD Sasahara, T. “Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$”. International Electronic Journal of Geometry 14/2 (Ekim 2021), 305-312. https://doi.org/10.36890/iejg.936026.
JAMA Sasahara T. Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$. Int. Electron. J. Geom. 2021;14:305–312.
MLA Sasahara, T. “Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$”. International Electronic Journal of Geometry, c. 14, sy. 2, 2021, ss. 305-12, doi:10.36890/iejg.936026.
Vancouver Sasahara T. Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$. Int. Electron. J. Geom. 2021;14(2):305-12.