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Complex Premanifolds and Foliations

In: Deformations of Mathematical Structures

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  • Włodzimierz Waliszewski

    (Polish Academy of Sciences, Institute of Mathematics)

Abstract

The concept of a complex premanifold (c.p.) as well as the concept of an analytical mapping of c.p. are introduced in the paper. In the category of c.p. for any set of complex functions there exist the smallest c.p. containing this set. Any complex manifold is a c.p. Some characterization of a complex submanifold of Cn is given and it is shown that if Cartesian product of two c.p. is a complex manifold, then these c.p. are complex manifolds as well. The paper concludes with considerations concerning foliations on c.p. The concept of such objects is defined and it is proved that if c.p. is a complex manifold, then on this manifold any foliation in the new sense is the foliation in the classical sense.

Suggested Citation

  • Włodzimierz Waliszewski, 1989. "Complex Premanifolds and Foliations," Springer Books, in: Julian Ławrynowicz (ed.), Deformations of Mathematical Structures, pages 65-78, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-2643-1_7
    DOI: 10.1007/978-94-009-2643-1_7
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