Graded Lie algebra of Hermitian tangent valued forms
| Authors | |
|---|---|
| Year of publication | 2006 |
| Type | Article in Periodical |
| Magazine / Source | Journal de Mathematiques Pures et Appliquees |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=6148&_auth=y&_acct=C000045159&_version=1&_urlVersion=0&_userid=835458&md5=043722a585bfa26d973fc7f7a2a6dad9 |
| Field | General mathematics |
| Keywords | Hermitian tangent valued forms; Froehlicher-Nijenhuis bracket |
| Description | 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. |
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