Natural parallel translation and connection associated to navigation data
Asma Mezrag, Zoltan Muzsnay, Csaba Vincze
TL;DR
This paper introduces a natural parallel translation in navigation data geometry using Riemannian parallelism, highlighting its homogeneous, norm-preserving, and finite-dimensional holonomy properties, contributing to geometric understanding in navigation contexts.
Contribution
It presents a novel natural parallel translation framework in navigation data geometry based on Riemannian parallelism, with distinctive properties.
Findings
The parallel translation is homogeneous and nonlinear.
It preserves the Randers type Finslerian norm.
The holonomy group is finite-dimensional.
Abstract
In this paper, we consider the geometric setting of navigation data and introduce a natural parallel translation using the Riemannian parallelism. The geometry obtained in this way has some nice and natural features: the natural parallel translation is homogeneous (but in general nonlinear), preserves the Randers type Finslerian norm constituted by the navigation data, and the holonomy group is finite-dimensional.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows · Fixed Point Theorems Analysis