In this article, we consider (M^n, g(t)) an n-dimensional closed Riemannian manifold whose metric g(t) evolves by the abstract geometric flow and the geometric constant \lambda_a^b as the lowest constant such that the equation

    \[- \Delta u + a u \log u + b S u = \lambda_a^b u\]

with \int_M u^2 d\mu = 1 has a positive solution, where a\ (>0) and b are two real constants. Here we find the evolution formula for \lambda_a^b on (M^n, g(t)) evolving along the abstract geometric flow.


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 Azami, Shahroud,  Saha, Apurba , Hui, Shyamal Kumar, Pişcoran, Laurian-Ioan