Classification of homogeneous holomorphic two-spheres in complex Grassmann manifolds

Jie Fei

doi:10.1016/j.difgeo.2018.09.005

Classification of homogeneous holomorphic two-spheres in complex Grassmann manifolds

Jie Fei

Department of Pure Mathematics

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

8 Citations (Scopus)

Abstract

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).

Original language	English
Pages (from-to)	1-38
Number of pages	38
Journal	Differential Geometry and its Application
Volume	62
DOIs	https://doi.org/10.1016/j.difgeo.2018.09.005
Publication status	Published - Feb 2019

Keywords

Gaussian curvature
Homogeneous holomorphic two-spheres
The second fundamental form
Veronese surfaces

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10.1016/j.difgeo.2018.09.005

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abstract = "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).",

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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 - https://www.scopus.com/pages/publications/85054094438

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DO - 10.1016/j.difgeo.2018.09.005

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SN - 0926-2245

VL - 62

SP - 1

EP - 38

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

ER -

Classification of homogeneous holomorphic two-spheres in complex Grassmann manifolds

Abstract

Keywords

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