Local (Sub)-Finslerian Geometry for the Maximum Norms in Dimension 2 View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-11

AUTHORS

Entisar Abdul-Latif Ali, Grégoire Charlot

ABSTRACT

We consider specific sub-Finslerian structures in the neighborhood of 0 in ℝ2, defined by fixing a family of vector fields (F1,F2) and considering the norm defined on the non-constant rank distribution Δ = vect{F1, F2} by |G|=infu{max{|u1|,|u2|}|G=u1F1+u2F2}. If F1 and F2 are not proportional at p, then we obtain a Finslerian structure; if not, the structure is sub-Finslerian on a distribution with non-constant rank. We are interested in the study of the local geometry of these Finslerian and sub-Finslerian structures: generic properties, normal form, short geodesics, cut locus, switching locus, and small spheres. More... »

PAGES

1-34

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10883-019-09435-8

DOI

http://dx.doi.org/10.1007/s10883-019-09435-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112676906


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