Harmonic maps of compact Kähler manifolds to exceptional local symmetric spaces of Hodge type and holomorphic liftings to complex homogeneous fibrations

TitleHarmonic maps of compact Kähler manifolds to exceptional local symmetric spaces of Hodge type and holomorphic liftings to complex homogeneous fibrations
Publication TypeJournal Article
Year of Publication2002
AuthorsKasparian A
JournalAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Volume94
Pagination97-121
Keywordsabelian subspaces, complex homogeneous fibrations, equivariant Hermitian symmetric subspaces, exceptional Riemannian symmetric spaces of Hodge type, harmonic and holomorphic maps, Levi-Civita connections
Abstract

Let $M$ be a compact $K\ddot{a}hler$ manifold and $G/K$ be a non-Hermitian Riemannian symmetric space of Hodge type. Certain harmonic maps $f : M \rightarrow \Gamma \setminus G / K$ will be proved to admit holomorphic liftings $F_p : M \rightarrow \Gamma \setminus G / G \cap P$ to complex homogeneous fibrations, where $P$ are parabolic subgroups of $G^\mathbb{C}$. The work studies whether the images $F_P(M)=\Gamma_h \setminus G_h/K_h$ are local equivariantly embedded Hermitian symmetric subspaces of $\Gamma \setminus G / G \cap P$. For each of the cases examples of harmonic maps $f$ which do not holomorphic liftings are supplied.

2000 MSC

58E20, 53C35, 22E30, 32H02

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