  Catanese and Franciosi defined a semispecial tensor as a (non zero) section
of the n-th symmetric power of the cotangent bundle twisted by the
anticanonical divisor and by a 2-torsion line bundle. A slope zero tensor is
instead a section of the nm-th symmetric power of the cotangent bundle twisted
by m times the anticanonical divisor. With these definitions we have: Theorem
1. The universal cover of X is the polydisk iff 1) holds. 1) X has ample
canonical bundle and admits a semispecial tensor such that at some point p the
corresponding hypersurface in the projectivized tangent space is reduced.
Theorem 2. If X has ample canonical bundle it admits a slope zero tensor if and
only if the universal cover of X is a bounded symmetric domain D of tube type.
The domain D is determined by the multiplicities of the irreducible components
of the corresponding tangential hypersurface. We have then a corollary which
extends previous results by Kazhdan. Corollary. Assume that the universal
covering of X is a bounded symmetric domain D of tube type. Let X^s be a Galois
conjugate of X : then also the universal cover of X^s is biholomorphic to D.
