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Revista de la
Unión Matemática Argentina
Evolution of first eigenvalues of some geometric operators under the rescaled List's extended Ricci flow
Shahroud Azami and Abimbola Abolarinwa

Volume 67, no. 2 (2024), pp. 529–543    

Published online (final version): October 9, 2024

https://doi.org/10.33044/revuma.3413

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Abstract

Let (M,g(t),e−ϕdν) be a compact weighted Riemannian manifold and let (g(t),ϕ(t)) evolve by the rescaled List's extended Ricci flow. In this paper, we study the evolution equations for first eigenvalues of the geometric operators, −Δϕ+cSa, along the rescaled List's extended Ricci flow. Here Δϕ=Δ−∇ϕ.∇ is a symmetric diffusion operator, ϕ∈C∞(M), S=R−α|∇ϕ|2, R is the scalar curvature with respect to the metric g(t) and a,c are some constants. As an application, we obtain some monotonicity results under the rescaled List's extended Ricci flow.

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