Diffeological Smoothness in Hodge Theory

2009/11/16 by Li, Jiayong
#Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.0911.3152

Abstract

On a compact, oriented, Riemannian manifold, the Hodge decomposition theorem associates a smooth primitive to any exact smooth form omega. In this paper, we show that given a smooth family of exact smooth forms omega(t), the family of associated primitives is also a smooth family with respect to t.

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