Principles of Locally Conformally Kähler Geometry (Record no. 59643)
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| fixed length control field | 06013nam a22005535i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-58120-5 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030112027.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240503s2024 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783031581205 |
| -- | 978-3-031-58120-5 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-031-58120-5 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA641-670 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBMP |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT012030 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBMP |
| Source | thema |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Ornea, Liviu. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 76374 |
| 245 10 - TITLE STATEMENT | |
| Title | Principles of Locally Conformally Kähler Geometry |
| Medium | [electronic resource] / |
| Statement of responsibility, etc. | by Liviu Ornea, Misha Verbitsky. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2024. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer Nature Switzerland : |
| -- | Imprint: Birkhäuser, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XXI, 736 p. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Progress in Mathematics, |
| International Standard Serial Number | 2296-505X ; |
| Volume/sequential designation | 354 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Introduction -- Part I: Lectures in locally conformally Kähler geometry -- Kähler manifolds -- Connections in vector bundles and the Froebenius theorem -- Locally conformally Kahler manifolds -- Hodge theory on complex manifolds and Vaisman's theorem -- Holomorphic vector bundles -- CR, Contact and Sasakian manifolds -- Vaisman manifolds -- The structure of compact Vaisman manifolds -- Orbifolds -- Quasi-regular foliations -- Regular and quasi-regular Vaisman manifolds -- LCK manifolds with potential -- Embedding LCK manifolds with potential in Hopf manifolds -- Logarithms and algebraic cones -- Pseudoconvex shells and LCK metrics on Hopf manifolds -- Embedding theorem for Vaisman manifolds -- Non-linear Hopf manifolds -- Morse-Novikov and Bott-Chern cohomology of LCK manifolds -- Existence of positive potentials -- Holomorphic S^1 actions on LCK manifolds -- Sasakian submanifolds in algebraic cones -- Oeljeklaus-Toma manifolds -- Appendices -- Part II: Advanced LCK geometry -- Non-Kähler elliptic surfaces -- Kodaira classification for non-Kähler complex surfaces -- Cohomology of holomorphic bundles on Hopf manifolds -- Mall bundles and flat connections on Hopf manifolds -- Kuranishi and Teichmüller spaces for LCK manifolds with potential -- The set of Lee classes on LCK manifolds with potential -- Harmonic forms on Sasakian and Vaisman manifolds -- Dolbeault cohomology of LCK manifolds with potential -- Calabi-Yau theorem for Vaisman manifolds -- Holomorphic tensor fields on LCK manifolds with potential -- Part III: Topics in locally conformally Kähler geometry -- Twisted Hamiltonian actions and LCK reduction -- Elliptic curves on Vaisman manifolds -- Submersions and bimeromorphic maps of LCK manifolds -- Bott-Chern cohomology of LCK manifolds with potential -- Hopf surfaces in LCK manifolds with potential -- Riemannian geometry of LCK manifolds -- Einstein-Weyl manifolds and the Futaki invariant -- LCK structures on homogeneous manifolds -- LCK structures on nilmanifolds and solvmanifolds -- Explicit LCK metrics on Inoue surfaces -- More on Oeljeklaus-Toma manifolds -- Locally conformally parallel and non-parallel structures -- Open questions. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | This monograph introduces readers to locally conformally Kähler (LCK) geometry and provides an extensive overview of the most current results. A rapidly developing area in complex geometry dealing with non-Kähler manifolds, LCK geometry has strong links to many other areas of mathematics, including algebraic geometry, topology, and complex analysis. The authors emphasize these connections to create a unified and rigorous treatment of the subject suitable for both students and researchers. Part I builds the necessary foundations for those approaching LCK geometry for the first time with full, mostly self-contained proofs and also covers material often omitted from textbooks, such as contact and Sasakian geometry, orbifolds, Ehresmann connections, and foliation theory. More advanced topics are then treated in Part II, including non-Kähler elliptic surfaces, cohomology of holomorphic vector bundles on Hopf manifolds, Kuranishi and Teichmüller spaces for LCK manifolds with potential, and harmonic forms on Sasakian and Vaisman manifolds. Each chapter in Parts I and II begins with motivation and historic context for the topics explored and includes numerous exercises for further exploration of important topics. Part III surveys the current research on LCK geometry, describing advances on topics such as automorphism groups on LCK manifolds, twisted Hamiltonian actions and LCK reduction, Einstein-Weyl manifolds and the Futaki invariant, and LCK geometry on nilmanifolds and on solvmanifolds. New proofs of many results are given using the methods developed earlier in the text. The text then concludes with a chapter that gathers over 100 open problems, with context and remarks provided where possible, to inspire future research. . |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 69684 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 72222 |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 69686 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 72225 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Verbitsky, Misha. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 76375 |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031581199 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031581212 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031581229 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Progress in Mathematics, |
| International Standard Serial Number | 2296-505X ; |
| Volume number/sequential designation | 354 |
| 9 (RLIN) | 74786 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-031-58120-5">https://doi.org/10.1007/978-3-031-58120-5</a> |
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| -- | ZDB-2-SMA |
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| -- | ZDB-2-SXMS |
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