Invariant structures on Lie groups and homogeneous manifolds
Articles
Publication Date: 2025
Journal Of Function Spaces (23148888)2025(1)
In this paper, we introduce cyclic (noncyclic) relatively Jaggi nonexpansive mappings on Busemann convex spaces and investigate the existence of their best proximity points (pairs). Furthermore, we extend the notation of relatively u-continuous mappings in geodesic spaces and generalize an existence result of best proximity points from strictly convex Banach spaces to Busemann convex spaces. We also generalize Ky Fan’s best approximation theorem using Schauder’s fixed-point theorem within the framework of Busemann convex spaces. Finally, we examine the existence of common points for a family of relatively u-continuous cyclic compact mappings in Busemann convex spaces, effectively generalizing the Markov–Kakutani theorem. Copyright © 2025 M. Gabeleh et al. Journal of Function Spaces published by John Wiley & Sons Ltd.
Publication Date: 2025
Indian Journal of Pure and Applied Mathematics (00195588)
A natural extension of a homogeneous geodesic in homogeneous Riemannian spaces G/H, known as a two-step homogeneous geodesic, can be expressed in the form γ(t)=π(exp(tx)exp(ty)), where x and y are elements of the Lie algebra of G. This paper aims to expand this concept to homogeneous Finsler spaces. We provide certain sufficient conditions for (α,β) spaces and decomposable cubic spaces to possess a one-parameter family of invariant Finsler metrics that can be classified as two-step Finsler geodesic orbit spaces. Additionally, we present some illustrative examples of these spaces. © The Indian National Science Academy 2025.
Publication Date: 2024
Journal of the Iranian Mathematical Society (27171612)5(2)pp. 243-252
In 2002, using a variational method, Lauret classified five-dimensional nilsolitons. In this work, using the algebraic Ricci soliton equation, we obtain the same classification. We show that, among ten classes of five-dimensional connected and simply connected nilmanifolds, seven classes admit the Ricci soliton structure. Furthermore, we compute the derivation that satisfies the algebraic Ricci soliton equation in each case.. © 2024 Iranian Mathematical Society.
Publication Date: 2024
Quaestiones Mathematicae (1727933X)47(8)pp. 1559-1570
In this paper, we give the flag curvature formula of general (α, β)-metrics of Berwald type. We study conformally related (α, β)-metrics, especially general (α, β)-metrics that are conformally related to invariant (α, β)-metrics. Also, a necessary and sufficient condition for a Finsler metric conformally related to an (α, β)-metric is given and conformally related Douglas Randers metrics are studied. Finally, we present some examples of conformally related (α, β)-metrics. © 2024 NISC (Pty) Ltd.
