Luis Fernandez (City University of New York)
The Dirac operator in the Clifford bundle and Kaehler identities for almost complex manifolds
We use the Dirac operator in the Clifford bundle of an almost complex manifold to obtain a different formulation of the Kaehler identities which, when viewed in the exterior bundle, give the known generalization of these identities for complex manifolds found by Demailly, thus obtaining a generalization of the Kaeher identities for almost complex manifolds. This result was also proved by de la Ossa, Karigiannis, and Svanes.
In the process we will define a number of operators in the Clifford bundle, together with relations between them, that should give an alternative way to study almost complex manifolds.
All the work presented is joint with Sam Hosmer.
MC 5417