The Bott-Chern cohomology groups and the Bott-Chern Laplacian on differential forms of mixed type on a compact foliated Kähler manifold are defined and studied. Also, a Hodge decomposition theorem of Bott-Chern type for differential forms of mixed type is proved. Finally, the case of projectivized tangent bundle of a complex Finsler manifold is discussed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm137-1-6,
author = {Cristian Ida},
title = {Hodge-Bott-Chern decompositions of mixed type forms on foliated K\"ahler manifolds},
journal = {Colloquium Mathematicae},
volume = {135},
year = {2014},
pages = {89-102},
zbl = {1317.53038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm137-1-6}
}
Cristian Ida. Hodge-Bott-Chern decompositions of mixed type forms on foliated Kähler manifolds. Colloquium Mathematicae, Tome 135 (2014) pp. 89-102. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm137-1-6/