TY - JOUR
T1 - Classification of homogeneous holomorphic two-spheres in complex Grassmann manifolds
AU - Fei, Jie
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2019/2
Y1 - 2019/2
N2 - In this paper we completely classify the linearly full homogeneous holomorphic two-spheres in the complex Grassmann manifolds G(2,N) and G(3,N). We also obtain the Gauss equation for the holomorphic immersions from a Riemann surface into G(k,N). By using which, we give explicit expressions of the Gaussian curvature and the square of the length of the second fundamental form of these homogeneous holomorphic two-spheres in G(2,N) and G(3,N).
AB - In this paper we completely classify the linearly full homogeneous holomorphic two-spheres in the complex Grassmann manifolds G(2,N) and G(3,N). We also obtain the Gauss equation for the holomorphic immersions from a Riemann surface into G(k,N). By using which, we give explicit expressions of the Gaussian curvature and the square of the length of the second fundamental form of these homogeneous holomorphic two-spheres in G(2,N) and G(3,N).
KW - Gaussian curvature
KW - Homogeneous holomorphic two-spheres
KW - The second fundamental form
KW - Veronese surfaces
UR - http://www.scopus.com/inward/record.url?scp=85054094438&partnerID=8YFLogxK
U2 - 10.1016/j.difgeo.2018.09.005
DO - 10.1016/j.difgeo.2018.09.005
M3 - Article
AN - SCOPUS:85054094438
SN - 0926-2245
VL - 62
SP - 1
EP - 38
JO - Differential Geometry and its Application
JF - Differential Geometry and its Application
ER -