Date of Degree
Geometry and Topology
Almost Hermitian Geometry
In 1980 Michelsohn defined a differential operator on sections of the complex Clifford bundle over a compact Kähler manifold M. This operator is a differential and its Laplacian agrees with the Laplacian of the Dolbeault operator on forms through a natural identification of differential forms with sections of the Clifford bundle. Relaxing the condition that M be Kähler, we introduce two differential operators on sections of the complex Clifford bundle over a compact almost Hermitian manifold which naturally generalize the one introduced by Michelsohn. We show surprising Kähler- like symmetries of the kernel of the Laplacians of these operators in the almost Hermitian and almost Kähler settings, along with a correspondence of these operators to operators on forms which are of present interest in almost complex geometry.
Hosmer, Samuel L., "Clifford Harmonics" (2021). CUNY Academic Works.