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Holomorphic last multipliers on complex manifolds |
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| Authors: | Mircea Crasmareanu Cristian Ida Paul Popescu |
| Affiliation: | 1. Faculty of Mathematics, University “Al. I. Cuza”, Ia?i, 700506, Bd. Carol I, no. 11, Romania;2. Department of Mathematics and Computer Science, University Transilvania of Bra?ov, Bra?ov 500091, Str. Iuliu Maniu 50, Romania;3. Department of Applied Mathematics, University of Craiova, Craiova, 200585, Str. Al. Cuza, no 13, Romania |
| Abstract: | The goal of this paper is to study the theory of last multipliers in the framework of complex manifolds with a fixed holomorphic volume form. The motivation of our study is based on the equivalence between a holomorphic ODE system and an associated real ODE system and we are interested how we can relate holomorphic last multipliers with real last multipliers. Also, we consider some applications of our study for holomorphic gradient vector fields on holomorphic Riemannain manifolds as well as for holomorphic Hamiltonian vector fields and holomorphic Poisson bivector fields on holomorphic Poisson manifolds. |
| Keywords: | Last multiplier complex manifold holomorphic volume form Poisson structure |