Evolution of Functionals Under Extended Ricci Flow

Abstract

In this paper, we investigate the evolution of certain functionals involving higher powers of a scalar quantity F under Bernard List’s extended Ricci flow on a compact Riemannian manifold. By deriving explicit expressions for the time derivative of integrals of the form R M F n · ∂F ∂t dµ for various powers n, we explore the intricate interplay between geometric quantities and scalar functions without making any assumptions about the manifold, the scalar field Φ, or the function u