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@article{634888,
author = {Janyška, Josef and Modugno, Marco},
article_location = {Francie},
article_number = {5},
keywords = {Hermitian tangent valued forms; Froehlicher-Nijenhuis bracket},
language = {eng},
issn = {0021-7824},
journal = {Journal de Mathematiques Pures et Appliquees},
title = {Graded Lie algebra of Hermitian tangent valued forms},
url = {http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=6148&_auth=y&_acct=C000045159&_version=1&_urlVersion=0&_userid=835458&md5=043722a585bfa26d973fc7f7a2a6dad9},
volume = {85},
year = {2006}
}
TY - JOUR
ID - 634888
AU - Janyška, Josef - Modugno, Marco
PY - 2006
TI - Graded Lie algebra of Hermitian tangent valued forms
JF - Journal de Mathematiques Pures et Appliquees
VL - 85
IS - 5
SP - 687-697
EP - 687-697
PB - Elsevier SAS
SN - 00217824
KW - Hermitian tangent valued forms
KW - Froehlicher-Nijenhuis bracket
UR - http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=6148&_auth=y&_acct=C000045159&_version=1&_urlVersion=0&_userid=835458&md5=043722a585bfa26d973fc7f7a2a6dad9
N2 - We define the Hermitian tangent valued forms of a complex 1-dimensional line bundle equipped with a Hermitian metric. We provide a local characterisation of these forms in terms of a local basis and of a local fibred chart. We show that these forms constitute a graded Lie algebra through the Froelicher-Nijenhuis bracket. Moreover, we provide a global characterisation of this graded Lie algebra, via a given Hermitian connection, in terms of the tangent valued forms and forms of the base space. The bracket involves the curvature of the given Hermitian connection.
ER -
JANYŠKA, Josef and Marco MODUGNO. Graded Lie algebra of Hermitian tangent valued forms. \textit{Journal de Mathematiques Pures et Appliquees}. Francie: Elsevier SAS, 2006, vol.~85, No~5, p.~687-697. ISSN~0021-7824.
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