Degree of constantly curved holomorphic 2-spheres in the complex Grassmannians G(2,n+2;C)
Ling He
TL;DR
This paper investigates the degrees of holomorphic 2-spheres with constant curvature in complex Grassmannians, establishing bounds that depend on the dimension n, thus advancing understanding of their geometric properties.
Contribution
It provides new bounds on the degrees of such holomorphic 2-spheres in G(2,n+2;C), extending known results for specific cases to general n.
Findings
Degree ≥ n for general n
Degree ≤ 2n for n=2,3
Bounds depend on the dimension n
Abstract
We show that the degree of the linearly full constantly curved holomorphic 2-spheres in the complex Grassmannians G(2,n+2;C) is greater than or equal to n for general n and less than or equal to 2n for n=2,3.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometric and Algebraic Topology