Title | Harmonic maps of compact Kähler manifolds to exceptional local symmetric spaces of Hodge type and holomorphic liftings to complex homogeneous fibrations |
Publication Type | Journal Article |
Year of Publication | 2002 |
Authors | Kasparian A |
Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Volume | 94 |
Pagination | 97-121 |
Keywords | abelian 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 |
Attachment | Size |
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94-097-121.pdf | 2.65 MB |