Beitr\"age zur Algebra und Geometrie Contributions to Algebra and Geometry Volume 35 (1994), No. 2, 283-314. Applications of Spectral Geometry to Affine and Projective Geometry Neda Bokan, Peter B. Gilkey, Udo Simon Abstract. We use the asymptotics of the heat equation to construct spectral invariants in affine and projective geometry. MSC 1991: 53A15, 53B05, 53C07, 53C40, 58G25.