On generalized $ξ$-Parallel Maps

Ahmed Mohammed Cherif

On generalized $ξ$-Parallel Maps

Differential Geometry 2026-07-11 v1

Authors: Ahmed Mohammed Cherif

Abstract

In this paper, we introduce and study the notion of generalized $\xi$ -parallel maps between Riemannian manifolds, where $\xi$ 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 $\xi$ -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 $\xi$ -parallel curves in space forms and examine generalized $\xi$ -parallel submanifolds of space forms admitting concircular vector fields.

Cite

@article{arxiv.2607.10292,
  title  = {On generalized $ξ$-Parallel Maps},
  author = {Ahmed Mohammed Cherif},
  journal= {arXiv preprint arXiv:2607.10292},
  year   = {2026}
}