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

• Autore: Chen Bang-Yen
• Pubblicazione: Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2025
• Edizione: 1st ed. 2025.
• Descrizione fisica: 1 online resource (959 pages)
• Disciplina: 516.36
• Soggetto topico: Geometry, Differential; Global analysis (Mathematics); Manifolds (Mathematics); Differential Geometry; Global Analysis and Analysis on Manifolds
• Altri autori: ShahidMohammad Hasan VîlcuGabriel-Eduard
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Geometry of CR-Submanifolds and Applications
• ISBN: 981-9628-18-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9911022467303321
• Lo trovi qui: Univ. Federico II
• Serie: Infosys Science Foundation Series in Mathematical Sciences, . 2364-4044