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As is known, the Blaschke tensor $A$ (a symmetric covariant $2$-tensor) isone of the fundamental M\"obius invariants in the M\"obius differentialgeometry of submanifolds in the unit sphere $\mathbb S^n$, and the eigenvaluesof $A$ are referred to as the Blaschke eigenvalues. In this paper, we continueour job for the study on the submanifolds in $\bbs^n$ with parallel Blaschketensors which we simply call {\em Blaschke parallel submanifolds} to find moreexamples and seek a complete classification finally. The main theorem of thispaper is the classification of Blaschke parallel submanifolds in $\mathbb S^n$with exactly three distinct Blaschke eigenvalues. Before proving thisclassification we define, as usual, a new class of examples.

On the immersed submanifolds in the unit sphere with parallel Blaschke tensor II