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arXiv · 2607.10292

On generalized $\xi$-Parallel Maps

Ahmed Mohammed Cherif
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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.

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Ahmed Mohammed Cherif. 2026-07-11. On generalized $\xi$-Parallel Maps. https://arxiv.org/abs/2607.10292

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