论文标题
randers-minkowski空间的子手的标志曲率根据zermelo数据
The flag curvature of a submanifold of a Randers-Minkowski space in terms of Zermelo data
论文作者
论文摘要
本文的主要结果是在与其zermelo data $（H，W）$的不变性方面的Randers-Minkowski Space $（{\ Mathscr V}，F）$的标志曲率表达。更确切地说，这些不变的是截面曲率和第二个基本形式的正确定标量产品$ h $和Wind $ W $的某些预测。这种表达允许对带有标量标志曲率的亚体的有前途的表征，从riemannian数量角度来看，当考虑到高表面时，这似乎很容易接近。结果，我们证明，任何$ H $ -Flat Hypersurface $ s $都有标量$ f $ -flag曲率，其Zermelo数据的指标在同一个方面都是平坦的。作为制定计算的工具，我们以前使用各向异性计算重新列出了伪渔脚架子manifold的高斯 - 库Zi方程。
The main result of this paper is an expression of the flag curvature of a submanifold of a Randers-Minkowski space $({\mathscr V},F)$ in terms of invariants related to its Zermelo data $(h,W)$. More precisely, these invariants are the sectional curvature and the second fundamental form of the positive definite scalar product $h$ and some projections of the wind $W$. This expression allows for a promising characterization of submanifolds with scalar flag curvature in terms of Riemannian quantities, which, when a hypersurface is considered, seems quite approachable. As a consequence, we prove that any $h$-flat hypersurface $S$ has scalar $F$-flag curvature and the metric of its Zermelo data is conformally flat. As a tool for making the computation, we previously reobtain the Gauss-Codazzi equations of a pseudo-Finsler submanifold using anisotropic calculus.
