Geometry of CR-Submanifolds and Applications / by Bang-Yen Chen, Mohammad Hasan Shahid, Gabriel-Eduard Vîlcu.

Format:

Book

Author/Creator:

Chen, Bang-yen.

Contributor:

Shahid, Mohammad Hasan.

Vîlcu, Gabriel-Eduard.

Series:

Infosys Science Foundation Series in Mathematical Sciences, 2364-4044

Language:

English

Subjects (All):

Geometry, Differential.

Global analysis (Mathematics).

Manifolds (Mathematics).

Differential Geometry.

Global Analysis and Analysis on Manifolds.

Local Subjects:

Differential Geometry.

Global Analysis and Analysis on Manifolds.

Physical Description:

1 online resource (959 pages)

Edition:

1st ed. 2025.

Place of Publication:

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

Summary:

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.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

981-9628-18-0

OCLC:

1544987465