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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 a Marco MODUGNO. Graded Lie algebra of Hermitian tangent valued forms. \textit{Journal de Mathematiques Pures et Appliquees}. Francie: Elsevier SAS, 2006, roč.~85, č.~5, s.~687-697. ISSN~0021-7824.
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