Harmonic Maps and Torse-Forming Vector Fields

Year 2020, Volume: 13 Issue: 1, 87 - 93, 30.01.2020

Ahmed Mohammed Cherif , Mustapha Djaa

https://doi.org/10.36890/iejg.555344

Abstract

In this paper, we prove that any harmonic map from a compact orientable Riemannian manifold
without boundary (or from complete Riemannian manifold) (M, g) to Riemannian manifold (N, h)
is necessarily constant, with (N, h) admitting a torse-forming vector field satisfying some condition.

Keywords

Harmonic maps , bi-harmonic maps , torse-forming vector fields

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