Year: 2026
Type: preprint
Abstract: In this paper, we introduce and study the notion of generalized $ξ$-parallel maps between Riemannian manifolds, where $ξ$ is a vector field on the target manifold. We define the associated energy functional and derive its first variation formula, leading to the Euler--Lagrange equation characterizing generalized $ξ$-parallel maps. We establish fundamental properties of this new class of maps and investigate its relationship with harmonic and biharmonic maps. Furthermore, we study generalized $ξ$-parallel curves in space forms and examine generalized $ξ$-parallel submanifolds of space forms admitting concircular vector fields.
Source: arXiv (Cornell University)
Author: Cherif, Ahmed Mohammed
Institution: Université Mustapha Stambouli de Mascara
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7168286403
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