Harmonic maps relative to α-connections of statistical manifolds
نویسنده
چکیده
In this paper, we study harmonic maps relative to α-connections, but not necessarily standard harmonic maps. A standard harmonic map is defined by the first variation of the energy functional of a map. A harmonic map relative to an α-connection is defined by an equation similar to a first variational equation, though it is not induced by the first variation of the standard energy functional. In this paper, we define energy functionals of maps relative to α-connections of statistical manifolds. Next, we show that, for harmonic maps relative to α-connections, the Euler-Lagrange equations are induced by first variations of energy functionals relative to α-connections.
منابع مشابه
Harmonic maps relative to α-connections on statistical manifolds
In this paper we study harmonic maps relative to α-connections, and not always relative to Levi-Civita connections, on statistical manifolds. In particular, harmonic maps on α-conformally equivalent statistical manifolds are discussed, and conditions for harmonicity are given by parameters α and dimensions n. As the application we also describe harmonic maps between level surfaces of a Hessian ...
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