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math.DG2023★ 1 cited
On the Existence of Parallel one Forms
Laszlo Kozma, Salah Gomaa Elgendi
In this paper, using the Finslerian settings, we study the existence of parallel one forms (or, equivalently parallel vector fields) on a Riemannian manifold. We show that a parall…
math.DG2023★ 2 cited
Hopf-Rinow Theorem of sub-Finslerian geometry
Layth M. Alabdulsada, Laszlo Kozma
The sub-Finslerian geometry means that the metric is defined only on a given subbundle of the tangent bundle, called a horizontal bundle. In the paper, a version of the Hopf-Ri…