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Rigidity of equivariant harmonic maps from the sphere into Grassmannians | Synapse

June 11, 2026Differential Geometry and its Applications0 citationsOpen Access

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Rigidity of equivariant harmonic maps from the sphere into Grassmannians

IKIsami KogaHiroshima University YNYasuyuki NagatomoKyushu University MTMasaro TakahashiNational Institute of Technology, Kurume College

Key Points

This research aims to demonstrate rigidity results for G-equivariant harmonic maps from the sphere into Grassmannians based on specific groups.
Proving rigidity results for equivariant harmonic maps
Analyzing maps into low rank real or complex Grassmannians
Considering cases for G = SO(m+1), Spin(m+1), G2 (m=6), and Spin(7) (m=7)
Demonstrated rigidity for equivariant harmonic maps into specified Grassmannians
Established unique geometric constraints associated with low rank Grassmannians
Confirmed the specified groups exhibit rigidity under the defined conditions

Abstract

We prove the rigidity results for G -equivariant harmonic maps of the sphere S m into real or complex Grassmannians of low rank for G = SO ( m + 1 ) , Spin ( m + 1 ) , G 2 (when m = 6 ) and Spin ( 7 ) (when m = 7 ).

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Cite This Study

Koga et al. (Tue,) studied this question.

synapsesocial.com/papers/6a2a505d80c8f91e7f39ce94 https://doi.org/https://doi.org/10.1016/j.difgeo.2026.102403