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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
In this case, F is a Berwald metric.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:The non-Riemannian quantity H was introduced by Akbar-Zadeh to characterization of Finsler metrics of constant flag curvature.
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Temel Bulgular & Veri:In this paper, we study two important subclasses of Finsler metrics in the class of so-called (α,β)-metrics, which are defined by F=αϕ(s), s=β/α, where α is a Riemannian metric and β is a closed 1-form on a manifold.
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Sonuç & Katkı:In this case, F is a Berwald metric.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Polynomial metrics · exponential metric · almost vanishing H-curvature
Abstract
The non-Riemannian quantity H was introduced by Akbar-Zadeh to characterization of Finsler metrics of constant flag curvature. In this paper, we study two important subclasses of Finsler metrics in the class of so-called (α,β)-metrics, which are defined by F=αϕ(s), s=β/α, where α is a Riemannian metric and β is a closed 1-form on a manifold. We prove that every polynomial metric of degree k≥3 and exponential metric has almost vanishing H-curvature if and only if H=0. In this case, F reduces to a Berwald metric. Then we prove that every Einstein polynomial metric of degree k≥3 and exponential metric satisfies H=0. In this case, F is a Berwald metric.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
TAYEBI, A., RAZGORDANI, M. (2020). On H-curvature of (α,β)-metrics. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 1, 207–222. https://ajindex.com/articles/193220