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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this article, we construct a new metric $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over G} = {}^R\nabla + \sum\limits_{i,j = 1}^m {a^{ji}} \delta {p_j}\delta {p_i}$ in the cotangent bundle, where ${}^R\nabla $ is the Riemannian extension and $ a^{ji}$ is a symmetric (2,0)-tensor field on a differentiable manifold.
📌 3 Key Takeaways
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Objective & Hypothesis:In this article, we construct a new metric $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over G} = {}^R\nabla + \sum\limits_{i,j = 1}^m {a^{ji}} \delta {p_j}\delta {p_i}$ in the cotangent bundle, where ${}^R\nabla $ is the Riemannian extension and $ a^{ji}$ is a symmetric (2,0)-tensor field on a differentiable manifold.
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Key Findings & Data:In this article, we construct a new metric $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over G} = {}^R\nabla + \sum\limits_{i,j = 1}^m {a^{ji}} \delta {p_j}\delta {p_i}$ in the cotangent bundle, where ${}^R\nabla $ is the Riemannian extension and $ a^{ji}$ is a symmetric (2,0)-tensor field on a differentiable manifold.
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Conclusion & Impact:In this article, we construct a new metric $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over G} = {}^R\nabla + \sum\limits_{i,j = 1}^m {a^{ji}} \delta {p_j}\delta {p_i}$ in the cotangent bundle, where ${}^R\nabla $ is the Riemannian extension and $ a^{ji}$ is a symmetric (2,0)-tensor field on a differentiable manifold.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cotangent bundle · Riemannian extension · geodesic
Abstract
In this article, we construct a new metric $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over G} = {}^R\nabla + \sum\limits_{i,j = 1}^m {a^{ji}} \delta {p_j}\delta {p_i}$ in the cotangent bundle, where ${}^R\nabla $ is the Riemannian extension and $ a^{ji}$ is a symmetric (2,0)-tensor field on a differentiable manifold.
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Cite This Article
Ocak, F. (2019). Notes About a New Metric on the Cotangent Bundle. International Electronic Journal of Geometry, Volume: 12 Issue: 2. https://doi.org/10.36890/iejg.542783