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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We also show that due to dualistic structure of the domain manifold the result is still valid in dual coordinates.
📌 3 Key Takeaways
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Objective & Hypothesis:We show an existence and uniqueness result for a class of maps from a flat statistical manifold into a Riemannian manifold in a given homotopy class when the target Riemannian manifold is of negative sectional curvature under a global topological non-triviality condition.
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Key Findings & Data:We show an existence and uniqueness result for a class of maps from a flat statistical manifold into a Riemannian manifold in a given homotopy class when the target Riemannian manifold is of negative sectional curvature under a global topological non-triviality condition.
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Conclusion & Impact:We also show that due to dualistic structure of the domain manifold the result is still valid in dual coordinates.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Statistical manifolds · dually flat structures · harmonic maps
Abstract
We show an existence and uniqueness result for a class of maps from a flat statistical manifold into a Riemannian manifold in a given homotopy class when the target Riemannian manifold is of negative sectional curvature under a global topological non-triviality condition. We also show that due to dualistic structure of the domain manifold the result is still valid in dual coordinates.
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Cite This Article
Şimşir, F. M. (2019). A note on harmonic maps of statistical manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 2. https://doi.org/10.31801/cfsuasmas.530449