TY - JOUR
T1 - Pinched Constantly Curved Holomorphic Two-Spheres in the Complex Grassmann Manifolds
AU - Fei, Jie
AU - Wang, Jun
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
PY - 2024/8
Y1 - 2024/8
N2 - In the recent paper (Wang et al. in Differ Geom Appl 80:101840, 2022), the authors and Xu have established a Simons-type integral inequality for holomorphic curves in a complex Grassmann manifold G(k, N). In this paper, we completely classify holomorphic immersions from the two-sphere of constant curvature into G(3, N) with the norm of the second fundamental form satisfying the equality case of the inequality and prove that any such immersion can be decomposed as the “direct sum” of some “foundation stones” up to congruence.
AB - In the recent paper (Wang et al. in Differ Geom Appl 80:101840, 2022), the authors and Xu have established a Simons-type integral inequality for holomorphic curves in a complex Grassmann manifold G(k, N). In this paper, we completely classify holomorphic immersions from the two-sphere of constant curvature into G(3, N) with the norm of the second fundamental form satisfying the equality case of the inequality and prove that any such immersion can be decomposed as the “direct sum” of some “foundation stones” up to congruence.
KW - 53C42
KW - 53C55
KW - complex Grassmann manifolds
KW - constant curvature
KW - holomorphic two-spheres
KW - Primary 53C20
KW - Simons-type integral inequality
UR - http://www.scopus.com/inward/record.url?scp=85199214358&partnerID=8YFLogxK
U2 - 10.1007/s00025-024-02236-x
DO - 10.1007/s00025-024-02236-x
M3 - Article
AN - SCOPUS:85199214358
SN - 1422-6383
VL - 79
JO - Results in Mathematics
JF - Results in Mathematics
IS - 5
M1 - 209
ER -