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Non-Kähler complex surfaces and strongly pseudoconcave surfaces

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Non-Kähler complex surfaces and strongly pseudoconcave surfaces/ by Naohiko Kasuya.
Author:	Kasuya, Naohiko.
Published:	Singapore :Springer Nature Singapore : : 2025.,
Description:	x, 121 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Topology. -
Online resource:	https://doi.org/10.1007/978-981-96-3002-8
ISBN:	9789819630028

Non-Kähler complex surfaces and strongly pseudoconcave surfaces
Kasuya, Naohiko.

Non-Kähler complex surfaces and strongly pseudoconcave surfaces[electronic resource] /by Naohiko Kasuya. - Singapore :Springer Nature Singapore :2025. - x, 121 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8201. - SpringerBriefs in mathematics..

Chapter 1.Preliminaries -- Chapter 2. Compact Complex Surfaces -- Chapter 3. Elliptic Surfaces and Lefschetz Fibrations -- Chapter 4. Non-Kähler Complex Structures on R2 -- Chapter 5. Strongly Pseudoconvex Manifolds -- Chapter 6. Contact Structures -- Chapter 7. Strongly Pseudoconcave Surfaces and Their Boundaries.

The main themes of this book are non-Kähler complex surfaces and strongly pseudoconcave complex surfaces. Though there are several notable examples of compact non-Kähler surfaces, including Hopf surfaces, Kodaira surfaces, and Inoue surfaces, these subjects have been regarded as secondary to Kähler manifolds and strongly pseudoconvex manifolds. Recently, however, the existence of uncountably many non-Kähler complex structures on the 4-dimensional Euclidean space has been shown by Di Scala, Kasuya, and Zuddas through their construction. Furthermore, Kasuya and Zuddas' handlebody construction reveals that strongly pseudoconcave surfaces have flexibility with respect to both four-dimensional topology and boundary contact structures. These constructions are based on the knowledge of differential topology and contact geometry, and provide examples of fruitful applications of these areas to complex geometry. Thus, for (especially non-compact) non-Kähler complex surfaces and strongly pseudoconcave complex surfaces, it is not an exaggeration to say that the research is still in its infancy, with numerous areas yet to be explored and expected to develop in the future.

ISBN: 9789819630028

Standard No.: 10.1007/978-981-96-3002-8doiSubjects--Topical Terms:

633483
Topology.

LC Class. No.: QA649

Dewey Class. No.: 515.946

Non-Kähler complex surfaces and strongly pseudoconcave surfaces
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520 $a The main themes of this book are non-Kähler complex surfaces and strongly pseudoconcave complex surfaces. Though there are several notable examples of compact non-Kähler surfaces, including Hopf surfaces, Kodaira surfaces, and Inoue surfaces, these subjects have been regarded as secondary to Kähler manifolds and strongly pseudoconvex manifolds. Recently, however, the existence of uncountably many non-Kähler complex structures on the 4-dimensional Euclidean space has been shown by Di Scala, Kasuya, and Zuddas through their construction. Furthermore, Kasuya and Zuddas' handlebody construction reveals that strongly pseudoconcave surfaces have flexibility with respect to both four-dimensional topology and boundary contact structures. These constructions are based on the knowledge of differential topology and contact geometry, and provide examples of fruitful applications of these areas to complex geometry. Thus, for (especially non-compact) non-Kähler complex surfaces and strongly pseudoconcave complex surfaces, it is not an exaggeration to say that the research is still in its infancy, with numerous areas yet to be explored and expected to develop in the future.
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