On surfaces and their contours.
The paper deals with tensor fields which are semiconjugated with torse-forming vector fields. The existence results for semitorse-forming vector fields and for convergent vector fields are proved.
Let be a real inner product space of any dimension; and let be a -map relating any two tensor spaces on . We study the consequences imposed on the form of this function by the condition that its gradient should be skew-symmetric with respect to some pairs of indexes. Any such a condition is written as a system of linear partial differential equations, with constant coefficients, which is symmetric with respect to certain couples of independent variables. The solutions of these systems appear...
If is a Hodge manifold and we construct a canonical sequence of functions such that in the topology. These functions have a simple geometric interpretation in terms of the moment map and they are real algebraic, in the sense that they are regular functions when is regarded as a real algebraic variety. The definition of is inspired by Berezin-Toeplitz quantization and by ideas of Donaldson. The proof follows quickly from known results of Fine, Liu and Ma.