  I investigate on the number t of real eigenvectors of a real symmetric
tensor. In particular, given a homogeneous polynomial f of degree d in 3
variables, i prove that t is greater or equal than 2c+1, if d is odd and t is
greater or equal than max(3,2c+1), is d is even, where c is the number of ovals
of the locus of zeros of f; for binary forms, i prove that t is greater or
equal than the number of real roots of f. Moreover, the above inequalities are
the best possible for binary forms of any degree and for ternary cubic and
quartic forms.
