论文标题
各向同性矢量力场沿各向同性曲线完成的工作价值
The value of the work done by an isotropic vector force field along an isotropic curve
论文作者
论文摘要
在本文中，我们考虑了配备了Riemannian Metric $ g $和内态$ Q $的3维微分歧管$ M $，其第三个功率是身份，$ Q $是$ g $的等级式。这两个结构$ g $和$ q $都确定了$（m，g，q）$上的相关度量$ f $。公制$ f $是必不可少的，它在$ m $上的任意点$ p $上定义了切线空间中的各向同性向量。 物理力由向量场表示。我们调查其载体在$（m，g，q）$上的矢量的物理力。此外，这些向量是各向同性的，它们沿各向同性曲线起作用。我们研究了这种力量所做的体育工作。
In the present paper we consider a 3-dimensional differentiable manifold $M$ equipped with a Riemannian metric $g$ and an endomorphism $Q$, whose third power is the identity and $Q$ acts as an isometry on $g$. Both structures $g$ and $Q$ determine an associated metric $f$ on $(M, g, Q)$. The metric $f$ is necessary indefinite and it defines isotropic vectors in the tangent space $T_{p}M$ at an arbitrary point $p$ on $M$. The physical forces are represented by vector fields. We investigate physical forces whose vectors are in $T_{p}M$ on $(M, g, Q)$. Moreover, these vectors are isotropic and they act along isotropic curves. We study the physical work done by such forces.
