Year: 2025
Type: preprint
Abstract: We investigate certain immersions of constant curvature from Riemann surfaces into flag manifolds equipped with invariant metrics, namely primitive lifts associated to pseudoholomorphic maps of surfaces into complex Grassmannians. We prove that a primitive immersion from the two-sphere into the full flag manifold which has constant curvature with respect to \emph{at least one} invariant metric is unitarily equivalent to the primitive lift of a Veronese map, hence it has constant curvature with respect to \emph{all} invariant metrics. We prove a partial generalization of this result to the case where the domain is a general simply connected Riemann surface. On the way, we consider the problem of finding the invariant metric on the flag manifold, under a certain normalization condition, that maximizes the induced area of the two-sphere by a given primitive immersion.
Source: arXiv (Cornell University)
Authors: Pacheco, Rui, Rehman, Mehmood Ur
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979244797
Cites:
Cited by:
Related to: