Final answer:
IgD is the antibody not secreted in significant amounts by B cells; it remains membrane-bound and plays a role in B cell maturation and antigen recognition.
Step-by-step explanation:
The antibody that is not secreted by B cells in significant amounts is IgD. IgD is mostly present as a membrane-bound monomer on the surface of naïve B cells, where it primarily functions as an antigen receptor involved in the activation and maturation of B cells into plasma cells. Although IgD is essential for the antigen recognition process, it does not have a well-defined secretory role like the other antibody classes such as IgG, IgM, IgA, and IgE. Therefore, only trace amounts of IgD are detected in serum, generally originating from the degradation of old B cells.