An $ m $-modified conformal vector field $ \xi $ on a Riemannian manifold $ \big(N^{k}, g\big) $ is a generalization of a conformal vector field in the sense that an $ m $-modified conformal vector field $ \xi $ becomes a conformal vector field as $ m\rightarrow \infty $. An $ m $-modified conformal vector field $ \xi $ on a Riemannian manifold $ \big(N^{k}, g\big) $ is said to be trivial if $ \xi = 0 $. In this article, we obtained two triviality results for an $ m $-modified conformal vector field $ \xi $ on a compact and connected Riemannian manifold $ \big(N^{k}, g\big) $. Additionally, two results were obtained for the triviality of an $ m $-modified conformal vector field $ \xi $ on a noncompact, complete, and connected Riemannian manifold $ \big(N^{k}, g\big) $. Finally, we studied the $ m $-modified gradient conformal vector field $ \nabla f $ for compact and noncompact Riemannian manifolds. Three results were obtained on triviality of an $ m $-modified gradient conformal vector field $ \nabla f $ on a compact and connected Riemannian manifold $ \big(N^{k}, g\big) $, and one such result was obtained for an $ m $-modified gradient conformal vector field $ \nabla f $ on a noncompact and connected Riemannian $ k $-manifold $ \big(N^{k}, g\big) $.
Citation: Sharief Deshmukh, Nasser Bin Turki, Bang-Yen Chen, Tanveer Fatima. Properties of $ m $-modified conformal vector fields on a Riemannian manifold[J]. AIMS Mathematics, 2026, 11(9): 29774-29795. doi: 10.3934/math.20261181
An $ m $-modified conformal vector field $ \xi $ on a Riemannian manifold $ \big(N^{k}, g\big) $ is a generalization of a conformal vector field in the sense that an $ m $-modified conformal vector field $ \xi $ becomes a conformal vector field as $ m\rightarrow \infty $. An $ m $-modified conformal vector field $ \xi $ on a Riemannian manifold $ \big(N^{k}, g\big) $ is said to be trivial if $ \xi = 0 $. In this article, we obtained two triviality results for an $ m $-modified conformal vector field $ \xi $ on a compact and connected Riemannian manifold $ \big(N^{k}, g\big) $. Additionally, two results were obtained for the triviality of an $ m $-modified conformal vector field $ \xi $ on a noncompact, complete, and connected Riemannian manifold $ \big(N^{k}, g\big) $. Finally, we studied the $ m $-modified gradient conformal vector field $ \nabla f $ for compact and noncompact Riemannian manifolds. Three results were obtained on triviality of an $ m $-modified gradient conformal vector field $ \nabla f $ on a compact and connected Riemannian manifold $ \big(N^{k}, g\big) $, and one such result was obtained for an $ m $-modified gradient conformal vector field $ \nabla f $ on a noncompact and connected Riemannian $ k $-manifold $ \big(N^{k}, g\big) $.
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Sharief Deshmukh, Nasser Bin Turki, Bang-Yen Chen, Tanveer Fatima. Properties of $ m $-modified conformal vector fields on a Riemannian manifold[J]. AIMS Mathematics, 2026, 11(9): 29774-29795. doi: 10.3934/math.20261181
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