Harmonic Maps into Grassmannians

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


A harmonic map from a Riemannian manifold into a Grassmannian manifold is characterized by a vector bundle, a space of sections of the bundle and a Laplace operator [10]. This characterization can be considered a generalization of a theorem of Takahashi [11]. We apply our main result which generalizes a theorem of Do Carmo and Wallach [4] to describe moduli spaces of special classes of harmonic maps from compact reductive Riemannian homogeneous spaces into Grassmannians. As an application, we give an alternative proof of the theorem of Bando and Ohnita [1] which states the rigidity of the minimal immersion of the complex projective line into complex projective spaces. Moreover, a similar method yields rigidity of holomorphic isometric embeddings between complex projective spaces, which is part of Calabi’s result [2]. Finally, we give a description of moduli spaces of holomorphic isometric embeddings of the projective line into quadrics [9].


Modulus Space Vector Bundle Complex Projective Space Minimal Immersion Holomorphic Line Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author is grateful to O. Macia and M. Takahashi for their kind help.


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© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of MathematicsMeiji UniversityKanagawaJapan

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