Abstract
This chapter is dedicated to the study of an important class of codimension one foliations with singularities. It is the class of foliations given by closed 1-forms. We study their holonomy and some extension property. Starting with the holomorphic case we are to consider the meromorphic case, making use of the extension results. We study separately the cases of foliations given by closed holomorphic 1-forms and foliations given by closed meromorphic 1-forms.
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References
L.V. Alphors: Complex Analysis; 2nd. edition, MacGraw-Hill Book Company, 1996. International Student Edition.
R.C. Gunning; Introduction to Holomorphic Functions of Several Variables, Vol. II, Local Theory, Wadsworth & Brooks/Cole Advanced Books & Software, California, USA, 1990.
R. Gunning & H. Rossi: Analytic functions of several complex variables; Prentice Hall, Englewood Cliffs, NJ, 1965.
L. Hormander: An Introduction to Complex Analysis in Several Variables; 3rd ed., North-Holland, Amsterdam, 1990.
M. Spivak: A Comprehensive Introduction to Differential Geometry; Vol. 1, second edition, Publish or Perish, Berkeley, 1979.
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Scárdua, B. (2021). Holomorphic Foliations Given by Closed 1-Forms. In: Holomorphic Foliations with Singularities. Latin American Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-76705-1_5
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DOI: https://doi.org/10.1007/978-3-030-76705-1_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-76704-4
Online ISBN: 978-3-030-76705-1
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