Non-Kähler Complex Surfaces and Strongly Pseudoconcave Surfaces / by Naohiko Kasuya.

Format:

Book

Author/Creator:

Kasuya, Naohiko., Author.

Series:

SpringerBriefs in Mathematics, 2191-8201

Language:

English

Subjects (All):

Functions of complex variables.

Topology.

Several Complex Variables and Analytic Spaces.

Local Subjects:

Several Complex Variables and Analytic Spaces.

Topology.

Physical Description:

1 online resource (X, 121 p. 16 illus., 5 illus. in color.)

Edition:

1st ed. 2025.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2025.

Summary:

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.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9789819630028

9819630029

OCLC:

1509717048