2014/09/06 by Constantin M. Arcuş, C. M. Arcus, E. Peyghan +2 · 5 citations
Mathematics · Medicine · Physics and Astronomy · #Adjoint representation of a Lie algebra #Advanced Differential Geometry Research #Algebra over a field #Covariant derivative #Curvature #Differential geometry #Geodesic #Geometric Analysis and Curvature Flows #Geometry #Lie algebra #Lie algebroid #Lie conformal algebra #Lie derivative #Lie group #Mathematical analysis #Mathematics #Ophthalmology and Eye Disorders #Pure mathematics #Tangent #Tangent bundle #Tangent space #Type (biology) #math.DG
paper · pdf · doi:10.1063/1.4903256
published in Journal of Mathematical Physics 55(12) (American Institute of Physics)
arxiv created 2014/09/06 · openalex publication_date 2014/12/01 · arxiv updated 2014/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The geometry of the Lie algebroid generalized tangent bundle of a generalized Lie algebroid is developed. Formulas of Ricci type and identities of Cartan and Bianchi type are presented. Introducing the notion of geodesic of a mechanical ρ,η-system with respect to a (ρ, η)-spray, the Berwald (ρ, η)-derivative operator, and its mixed curvature, we obtain main results to conceptualize the Weyl’s method in this general framework. Finally, we obtain two new results of Weyl type for the geometry of mechanical ρ,η-systems. In this way, it is proved that the projectively related sprays first have the same geodesics rather to an increasing parameter transformation and second their Berwald derivatives verify a respective relation.