Harmonic Maps Relative to \(\alpha \)-Connections

  • Keiko UohashiEmail author
Part of the Signals and Communication Technology book series (SCT)


In this paper, we study harmonic maps relative to \(\alpha \)-connections, but not necessarily relative to Levi-Civita connections, on Hessian domains. For the purpose, we review the standard harmonic map and affine harmonic maps, and describe the conditions for harmonicity of maps between level surfaces of a Hessian domain in terms of the parameter \(\alpha \) and the dimension \(n\). To illustrate the theory, we describe harmonic maps between the level surfaces of convex cones.


Riemannian Manifold Level Surface Gradient Mapping Christoffel Symbol Hermitian Manifold 
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The author thanks the referees for their helpful comments.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Intelligent Systems, Faculty of EngineeringTohoku Gakuin UniversityTagajoJapan

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