A characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric

Jie Fei; Jun Wang; Xiaowei Xu

doi:10.1142/S0129167X23501008

A characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric

Jie Fei, Jun Wang^*, Xiaowei Xu

^*Corresponding author for this work

Xi'an Jiaotong-Liverpool University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we give a characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric Q_n. Let f be a totally real minimal immersion from two-sphere in Q_n, and τ_XY, τ_X_c (see Sec. 2) are globally defined invariants relative to the first and second fundamental forms. We prove that if its Gauss curvature K and τ_XY are constants, and τ_X_c vanishes identically, then f is congruent to F₂_k,₂_l constructed by the Boruvka spheres with n = 2(k + l).

Original language	English
Article number	2350100
Journal	International Journal of Mathematics
Volume	35
Issue number	1
DOIs	https://doi.org/10.1142/S0129167X23501008
Publication status	Published - 2024

Keywords

Constant curvature
homogeneity
hyperquadric
minimal two-spheres
totally real

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Fei, J., Wang, J., & Xu, X. (2024). A characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric. International Journal of Mathematics, 35(1), Article 2350100. https://doi.org/10.1142/S0129167X23501008

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abstract = "In this paper, we give a characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric Qn. Let f be a totally real minimal immersion from two-sphere in Qn, and τXY, τXc (see Sec. 2) are globally defined invariants relative to the first and second fundamental forms. We prove that if its Gauss curvature K and τXY are constants, and τXc vanishes identically, then f is congruent to F2k,2l constructed by the Boruvka spheres with n = 2(k + l).",

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N2 - In this paper, we give a characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric Qn. Let f be a totally real minimal immersion from two-sphere in Qn, and τXY, τXc (see Sec. 2) are globally defined invariants relative to the first and second fundamental forms. We prove that if its Gauss curvature K and τXY are constants, and τXc vanishes identically, then f is congruent to F2k,2l constructed by the Boruvka spheres with n = 2(k + l).

AB - In this paper, we give a characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric Qn. Let f be a totally real minimal immersion from two-sphere in Qn, and τXY, τXc (see Sec. 2) are globally defined invariants relative to the first and second fundamental forms. We prove that if its Gauss curvature K and τXY are constants, and τXc vanishes identically, then f is congruent to F2k,2l constructed by the Boruvka spheres with n = 2(k + l).

KW - Constant curvature

KW - homogeneity

KW - hyperquadric

KW - minimal two-spheres

KW - totally real

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JO - International Journal of Mathematics

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A characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric

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