For sphere bundles of the induced bundles of isometric immersions, harmonic sections which are normal to submanifolds and their index are studied. The lower bounds of the index of these sections are given in terms of intrinsic quantities of submanifolds.
"Harmonic Sections Normal to Submanifolds and Their Stability." Tokyo J. Math. 27 (2) 457 - 468, December 2004. https://doi.org/10.3836/tjm/1244208401