We define the Hermitian tangent valued forms of a complex I-dimensional line bundle equipped with a Hermitian metric. We provide a local characterization 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 Frolicher-Nijenhuis bracket. Moreover, we provide a global characterization 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.
Graded Lie algebra of Hermitian tangent valued forms / M. MODUGNO; J. JANYSKA. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 85:(2005), pp. 687-697. [10.1016/j.matpur.2005.11.004]
Graded Lie algebra of Hermitian tangent valued forms
MODUGNO, MARCO;
2005
Abstract
We define the Hermitian tangent valued forms of a complex I-dimensional line bundle equipped with a Hermitian metric. We provide a local characterization 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 Frolicher-Nijenhuis bracket. Moreover, we provide a global characterization 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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.