Abstract
AbstractLet $$(M,J,g,\omega )$$
(
M
,
J
,
g
,
ω
)
be a Kähler manifold. We prove a $$W^{1,2}$$
W
1
,
2
weak Bott-Chern decomposition and a $$W^{1,2}$$
W
1
,
2
weak Dolbeault decomposition of the space of $$W^{1,2}$$
W
1
,
2
differential (p, q)-forms, following the $$L^2$$
L
2
weak Kodaira decomposition on Riemannian manifolds. Moreover, if the Kähler metric is complete and the sectional curvature is bounded, the $$W^{1,2}$$
W
1
,
2
Bott-Chern decomposition is strictly related to the space of $$W^{1,2}$$
W
1
,
2
Bott-Chern harmonic forms, i.e., $$W^{1,2}$$
W
1
,
2
smooth differential forms which are in the kernel of an elliptic differential operator of order 4, called Bott-Chern Laplacian.
Funder
Università degli Studi di Parma
Publisher
Springer Science and Business Media LLC