Non-Kähler Complex Surfaces and Strongly Pseudoconcave Surfaces
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Beschreibung
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.
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.
Overviewing broad range of subjects Uniqueness of the strategy of original research results With the help of several figures, easier to read than author’s original papers
Autor*in
Naohiko Kasuya
Themen in »Non-Kähler Complex Surfaces and Strongly Pseudoconcave Surfaces«
Non-Kähler complex surface Lefschetz fibration Dehn surgery strong pseudoconvexity (pseudoconcavity) contact structure elliptic surface
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“Each topic is introduced with care, examples, and definitions, making the text accessible to graduate students and researchers alike. The exposition is concise yet self-contained, and the numerous cross-references between complex geometry, differential topology, and contact geometry make the volume a valuable resource for anyone working at their intersection.” (Wei Xia, zbMATH 1575.32001, 2026)
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