Vol. 25, No. 2, 1968

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Point norms in the construction of harmonic forms

Leo Sario and Mitsuru Nakai

Vol. 25 (1968), No. 2, 325–329
Abstract

Let V be an arbitrary Riemannian n-space, and V 1 a regular neighborhood of its ideal boundary. Given a harmonic field σ in V 1, necessary and sufficient conditions are known for the existence in V of a harmonic field ρ which imitates the behavior of σ in V 1 in the sense V 1(ρ σ) ∧∗(ρ σ) < . In the present paper we give the solution of the corresponding problem for harmonic forms in locally flat spaces.

Mathematical Subject Classification
Primary: 53.72
Secondary: 31.00
Milestones
Received: 25 July 1966
Published: 1 May 1968
Authors
Leo Sario
Mitsuru Nakai