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引用次数: 0
摘要
在这篇文章中,我们研究了前向完全芬斯勒流形中封闭(不一定紧凑)子流形的切点。我们探讨了切点的变形和特征,扩展了巴苏和普拉萨德(Algebr Geom Topol 23(9):4185-4233, 2023)的成果。给定子曲面 N,我们将 N 射线环视为起于和止于 N 的 N 射线,可能在不同的点。大森(Omori)曾研究过这类大地线(J Differ Geom 2:233-252, 1968)。我们得到了克林根伯格关于闭合大地线的通解(Klingenberg in:在可逆 Finsler 设置中的 N-大地环。
On the Cut Locus of Submanifolds of a Finsler Manifold
In this article, we investigate the cut locus of closed (not necessarily compact) submanifolds in a forward complete Finsler manifold. We explore the deformation and characterization of the cut locus, extending the results of Basu and Prasad (Algebr Geom Topol 23(9):4185–4233, 2023). Given a submanifold N, we consider an N-geodesic loop as an N-geodesic starting and ending in N, possibly at different points. This class of geodesics were studied by Omori (J Differ Geom 2:233–252, 1968). We obtain a generalization of Klingenberg’s lemma for closed geodesics (Klingenberg in: Ann Math 2(69):654–666, 1959). for N-geodesic loops in the reversible Finsler setting.