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On tensor fields semiconjugated with torse-forming vector fields

Lukáš Rachůnek, Josef Mikeš (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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.

On tensor functions whose gradients have some skew-symmetries

Adriano Montanaro (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let V n be a real inner product space of any dimension; and let Q α 1 α v = Q α 1 α v X β 1 β τ be a C 2 -map relating any two tensor spaces on V n . 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 α μ , β η 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...

On the approximation of functions on a Hodge manifold

Alessandro Ghigi (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

If ( M , ω ) is a Hodge manifold and f C ( M , ) we construct a canonical sequence of functions f N such that f N f in the C 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 M is regarded as a real algebraic variety. The definition of f N is inspired by Berezin-Toeplitz quantization and by ideas of Donaldson. The proof follows quickly from known results of Fine, Liu and Ma.

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