Date of Degree

9-2021

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Luis Fernandez

Committee Members

Scott Wilson

Mehdi Lejmi

Subject Categories

Geometry and Topology

Keywords

Almost Hermitian Geometry

Abstract

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.

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