Structure of geodesics in weakly symmetric Finsler metrics on H-type groups

Zdeněk Dušek

Address: Institute of Technology and Business in České Budějovice, Okružní 517/10, 370 01 České Budějovice, Czech Republic

E-mail: zdusek@mail.vstecb.cz

Abstract: Structure of geodesic graphs in special families of invariant weakly symmetric Finsler metrics on modified H-type groups is investigated. Geodesic graphs on modified H-type groups with the center of dimension $1$ or $2$ are constructed. The new patterns of algebraic complexity of geodesic graphs are observed.

AMSclassification: primary 53C22; secondary 53C60, 53C30.

Keywords: Finsler space, weakly symmetric space, g.o. space, homogeneous geodesic, geodesic graph.

DOI: 10.5817/AM2020-5-265