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Geometry of CR-submanifolds and applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometry of CR-submanifolds and applicationsby Bang-Yen Chen, Mohammad Hasan Shahid, Gabriel-Eduard Vîlcu.
Author:	Chen, Bang-Yen.
other author:	Shahid, Mohammad Hasan.
Published:	Singapore :Springer Nature Singapore :2025.
Description:	xxvi, 597 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	CR submanifolds.
Online resource:	https://doi.org/10.1007/978-981-96-2818-6
ISBN:	9789819628186$q(electronic bk.)

Geometry of CR-submanifolds and applications
Chen, Bang-Yen.

Geometry of CR-submanifolds and applications[electronic resource] /by Bang-Yen Chen, Mohammad Hasan Shahid, Gabriel-Eduard Vîlcu. - Singapore :Springer Nature Singapore :2025. - xxvi, 597 p. :ill., digital ;24 cm. - Infosys Science Foundation series in mathematical sciences,2364-4044. - Infosys Science Foundation series in mathematical sciences..

Chapter 1 Basics on Manifolds and Submanifolds -- Chapter 2 Basics on almost Hermitian manifolds and their subclasses -- Chapter 3 CR-submanifolds of K¨ahler manifolds -- Chapter 4 Inequalities for CR-submanifolds in Kähler manifolds -- Chapter 5 CR-warped products in Kähler manifolds -- Chapter 6 CR-submanifolds of locally conformal Kähler manifolds -- Chapter 7 CR-submanifolds of quaternion Kähler manifolds -- Chapter 8 CR-submanifolds of nearly Kähler manifolds -- Chapter 9CR-submanifolds of quasi-Kähler manifolds -- Chapter 10 Generic submanifolds of nearly Kähler manifolds -- Chapter 11 Generic submanifold of locally conformal Kähler manifolds -- Chapter 12 Basics of almost contact metric manifolds and their subclasses -- Chapter 13 Contact CR-submanifolds of trans-Sasakian manifolds -- Chapter 14 CContact CR-submanifolds of nearly Sasakian manifolds -- Chapter 15. Contact CR-submanifolds of nearly trans-Sasakian manifolds -- Chapter 16 Contact CR-submanifolds of quasi-Sasakian manifolds -- Chapter 17 Contact CR-submanifolds of ��-manifolds -- Chapter 18. Generic submanifolds of manifolds equipped with almost contactmetric structures -- Chapter 19. Submersion of CR-submanifolds -- Chapter 20 Contact CR-warped product submanifolds -- Chapter 22CR-submanifolds of indefinite K¨ahler manifolds and applications.

This book attempts to present a comprehensive survey of the geometry of CR-submanifolds. The theory of submanifolds is one of the most interesting topics in differential geometry. The topic is introduced by Aurel Bejancu as a generalization of holomorphic and totally real submanifolds of almost Hermitian manifolds, in 1978. Afterward, the study of CR-submanifolds became a very active research subject. Organized into 22 chapters, the book starts with basic knowledge of Riemannian manifolds and submanifolds, almost Hermitian manifolds and their subclasses, Hopf fibration, symmetric spaces, and a general inequality for submanifolds in complex space forms (in Chaps. 1 and 2). Later, it presents the main results on CR-submanifolds in Kaehler manifolds, the basic inequalities associated with CR-submanifolds in Kaehler manifolds, and several theories and results related to Kaehler manifolds (in Chaps. 3-11). Further, the book discusses the basics of almost-contact metric manifolds and their subclasses, CR-submanifolds of Sasakian, trans-Sasakian and quasi-Sasakian manifolds, with a particular attention on the normal CR-submanifolds (in Chap. 12). It also investigates the contact CR-submanifolds of S-manifolds, the geometry of submersions of CR-submanifolds, and the results on contact CR-warped product submanifolds (in Chaps. 16-18, 20). In Chapter 19, we discuss submersions of CR-submanifolds. The book also presents some recent results concerning CR-submanifolds of holomorphic statistical manifolds. In particular, it gives the classification of totally umbilical CR-statistical submanifolds in holomorphic statistical manifolds, as well as a Chen-Ricci inequality for such submanifolds (Chapter 21). In the last chapter, we present results on CR-submanifolds of indefinite Kaehler manifolds and their applications to physics.

ISBN: 9789819628186$q(electronic bk.)

Standard No.: 10.1007/978-981-96-2818-6doiSubjects--Topical Terms:

278593
CR submanifolds.

LC Class. No.: QA649

Dewey Class. No.: 516.36

Geometry of CR-submanifolds and applications
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505 0 $a Chapter 1 Basics on Manifolds and Submanifolds -- Chapter 2 Basics on almost Hermitian manifolds and their subclasses -- Chapter 3 CR-submanifolds of K¨ahler manifolds -- Chapter 4 Inequalities for CR-submanifolds in Kähler manifolds -- Chapter 5 CR-warped products in Kähler manifolds -- Chapter 6 CR-submanifolds of locally conformal Kähler manifolds -- Chapter 7 CR-submanifolds of quaternion Kähler manifolds -- Chapter 8 CR-submanifolds of nearly Kähler manifolds -- Chapter 9CR-submanifolds of quasi-Kähler manifolds -- Chapter 10 Generic submanifolds of nearly Kähler manifolds -- Chapter 11 Generic submanifold of locally conformal Kähler manifolds -- Chapter 12 Basics of almost contact metric manifolds and their subclasses -- Chapter 13 Contact CR-submanifolds of trans-Sasakian manifolds -- Chapter 14 CContact CR-submanifolds of nearly Sasakian manifolds -- Chapter 15. Contact CR-submanifolds of nearly trans-Sasakian manifolds -- Chapter 16 Contact CR-submanifolds of quasi-Sasakian manifolds -- Chapter 17 Contact CR-submanifolds of 𝑺-manifolds -- Chapter 18. Generic submanifolds of manifolds equipped with almost contactmetric structures -- Chapter 19. Submersion of CR-submanifolds -- Chapter 20 Contact CR-warped product submanifolds -- Chapter 22CR-submanifolds of indefinite K¨ahler manifolds and applications.
520 $a This book attempts to present a comprehensive survey of the geometry of CR-submanifolds. The theory of submanifolds is one of the most interesting topics in differential geometry. The topic is introduced by Aurel Bejancu as a generalization of holomorphic and totally real submanifolds of almost Hermitian manifolds, in 1978. Afterward, the study of CR-submanifolds became a very active research subject. Organized into 22 chapters, the book starts with basic knowledge of Riemannian manifolds and submanifolds, almost Hermitian manifolds and their subclasses, Hopf fibration, symmetric spaces, and a general inequality for submanifolds in complex space forms (in Chaps. 1 and 2). Later, it presents the main results on CR-submanifolds in Kaehler manifolds, the basic inequalities associated with CR-submanifolds in Kaehler manifolds, and several theories and results related to Kaehler manifolds (in Chaps. 3-11). Further, the book discusses the basics of almost-contact metric manifolds and their subclasses, CR-submanifolds of Sasakian, trans-Sasakian and quasi-Sasakian manifolds, with a particular attention on the normal CR-submanifolds (in Chap. 12). It also investigates the contact CR-submanifolds of S-manifolds, the geometry of submersions of CR-submanifolds, and the results on contact CR-warped product submanifolds (in Chaps. 16-18, 20). In Chapter 19, we discuss submersions of CR-submanifolds. The book also presents some recent results concerning CR-submanifolds of holomorphic statistical manifolds. In particular, it gives the classification of totally umbilical CR-statistical submanifolds in holomorphic statistical manifolds, as well as a Chen-Ricci inequality for such submanifolds (Chapter 21). In the last chapter, we present results on CR-submanifolds of indefinite Kaehler manifolds and their applications to physics.
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650 0 $a Geometry, Differential. $3 182610
650 1 4 $a Differential Geometry. $3 273785
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
700 1 $a Shahid, Mohammad Hasan. $3 747941
700 1 $a Vîlcu, Gabriel-Eduard. $3 1000167
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950 $a Mathematics and Statistics (SpringerNature-11649)