Open Access
June 2005 Pluriharmonic maps in affine differential geometryand $(1, 1)$-geodesic affine immersions
Hokkaido Math. J. 34(2): 459-488 (June 2005). DOI: 10.14492/hokmj/1285766232


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.


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Sanae KUROSU. "Pluriharmonic maps in affine differential geometryand $(1, 1)$-geodesic affine immersions." Hokkaido Math. J. 34 (2) 459 - 488, June 2005.


Published: June 2005
First available in Project Euclid: 29 September 2010

zbMATH: 1144.53309
MathSciNet: MR2159007
Digital Object Identifier: 10.14492/hokmj/1285766232

Primary: 53C15
Secondary: 53A15

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

Rights: Copyright © 2005 Hokkaido University, Department of Mathematics

Vol.34 • No. 2 • June 2005
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