Spectral geometry of totally complex submanifolds of QPⁿ

Abstract

We calculate some invariants determined by the spectrum of the Jacobi operator J of totally complex submanifolds of the quaternionic projective space QPⁿ. We use these invariants, and the ones determined by the spectrum of the Laplace-Beltrami operator Δ, to characterize parallel submanifolds of QPⁿ.