Hokkaido Mathematical Journal

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

Sanae KUROSU

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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.

Article information

Source
Hokkaido Math. J., Volume 34, Number 2 (2005), 459-488.

Dates
First available in Project Euclid: 29 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1285766232

Digital Object Identifier
doi:10.14492/hokmj/1285766232

Mathematical Reviews number (MathSciNet)
MR2159007

Zentralblatt MATH identifier
1144.53309

Subjects
Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Secondary: 53A15: Affine differential geometry

Keywords
pluriharmonic map $(1 1)$-geodesic affine immersion complex affine immersion

Citation

KUROSU, Sanae. Pluriharmonic maps in affine differential geometryand $(1, 1)$-geodesic affine immersions. Hokkaido Math. J. 34 (2005), no. 2, 459--488. doi:10.14492/hokmj/1285766232. https://projecteuclid.org/euclid.hokmj/1285766232


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