论文标题
Finslerian Geodesics在Fréchet歧管上
Finslerian geodesics on Fréchet manifolds
论文作者
论文摘要
我们建立了一个框架，即核边界的Fréchet歧管，并具有Riemann-Finsler结构，以在某些无限的尺寸歧管上研究地球曲线，例如Riemannian指标的歧管上的封闭歧管。我们证明了在本地存在的这些歧管，并且从某种意义上使它们最小化。此外，我们表明，当且仅当它满足Euler-Lagrange方程的集合时，这些歧管上的曲线是大地测量的。作为一种应用，我们毫不费力地证明了对爱因斯坦歧管上RICCI流动的解决方案不是大地的。
We establish a framework, namely, nuclear bounded Fréchet manifolds endowed with Riemann-Finsler structures to study geodesic curves on certain infinite dimensional manifolds such as the manifold of Riemannian metrics on a closed manifold. We prove on these manifolds geodesics exist locally and they are length minimizing in a sense. Moreover, we show that a curve on these manifolds is geodesic if and only if it satisfies a collection of Euler-Lagrange equations. As an application, without much difficulty, we prove that the solution to the Ricci flow on an Einstein manifold is not geodesic.
