 

O. GilMedrano and A. Montesinos Amilibia
About a Decomposition of the Space of Symmetric Tensors of Compact Support on a Riemannian Manifold


Published: 
July 13, 1994 
Keywords: 
manifold of Riemannian metrics, elliptic operators on noncompact manifolds, manifolds of maps 
Subject: 
Primary: 58D15, 58D17. Secondary: 58G25 


Abstract
Let M be a noncompact manifold and let Γ^{∞}_{c}(S^{2}(M))
(respectively Γ^{∞}_{c}(T^{1}(M))) be the LF space of 2covariant symmetric
tensor fields (resp. 1forms) on M, with compact support. Given any Riemannian metric g on
M, the firstorder differential
operator δ*:Γ^{∞}_{c}(T^{1}(M))→Γ^{∞}_{c}(S^{2}(M)) can be defined by
δ*ω = 2 symm∇ω, where ∇
denotes the LeviCivita connection of g.
The aim of this paper is to prove that the subspace
Im δ* is closed and to show several examples of
Riemannian manifolds for which
Γ^{∞}_{c}(S^{2}(M)) ≠ Im δ*
⊕ (Imδ*)^{⊥},
where orthogonal is taken with
respect to the usual inner product defined by the metric.


Author information
Departamento de Geometría y Topología. Facultad de
Matemáticas. Universidad de Valencia. 46100 Burjasot, Valencia. SPAIN.
Olga.Gil@uv.es
Angel.Montesinos@uv.es

