Hokkaido Mathematical Journal

KUROSU Sanae,

Pluriharmonic maps in affine differential geometryand $(1, 1)$-geodesic affine immersions.

Hokkaido Mathematical Journal, 34 (2005) pp.459-488

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Abstract

We define a pluriharmonic map from a complex manifold with a complex affine connection to a manifold with an affine connection and obtain some fundamental results which generalize those for a pluriharmonic map from a K\"{a}hler manifold to a Riemannian manifold. Especially, by using an associated family, we find a sufficient condition for the product of two $(1,1)$-geodesic affine immersions to an affine space to be a complex affine immersion from the manifold to the product of affine spaces with a certain complex structure.

MSC(Primary)53C15
MSC(Secondary)53A15
Uncontrolled Keywordspluriharmonic map, $(1, 1)$-geodesic affine immersion, complex affine immersion