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(2014) Geometric theory of information, Dordrecht, Springer.
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.
Publication details
DOI: 10.1007/978-3-319-05317-2_4
Full citation:
Uohashi, K. (2014)., Harmonic maps relative to $$alpha $$-connections, in F. Nielsen (ed.), Geometric theory of information, Dordrecht, Springer, pp. 81-96.
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