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Principles of locally conformally Kähler geometry

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Principles of locally conformally Kähler geometry/ by Liviu Ornea, Misha Verbitsky.
作者:	Ornea, Liviu.
其他作者:	Verbitsky, Misha.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	xxi, 736 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Kahlerian manifolds. -
電子資源:	https://doi.org/10.1007/978-3-031-58120-5
ISBN:	9783031581205

Principles of locally conformally Kähler geometry
Ornea, Liviu.

Principles of locally conformally Kähler geometry[electronic resource] /by Liviu Ornea, Misha Verbitsky. - Cham :Springer Nature Switzerland :2024. - xxi, 736 p. :ill., digital ;24 cm. - Progress in mathematics,v. 3542296-505X ;. - Progress in mathematics ;v. 354..

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.

ISBN: 9783031581205

Standard No.: 10.1007/978-3-031-58120-5doiSubjects--Topical Terms:

708349
Kahlerian manifolds.

LC Class. No.: QA649

Dewey Class. No.: 516.36

Principles of locally conformally Kähler geometry
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520 $a 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.
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