Geometry of CR-Submanifolds and Applications (eBook)
597 Seiten
Springer (Verlag)
978-981-96-2818-6 (ISBN)
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.
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.
| Erscheint lt. Verlag | 29.8.2025 |
|---|---|
| Reihe/Serie | Infosys Science Foundation Series | Infosys Science Foundation Series in Mathematical Sciences |
| Zusatzinfo | XXVI, 597 p. |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | contact CR-submanifold • contact CR warped product • CR product • CR statistical submanifold • CR-submanifolds • CR submersion • CR-wrapped products • Differential Geometry • generic submanifold • generic warped product • Hermitian manifolds • Kahler manifolds • locally conformal manifolds • Lorentzian CR-submanifolds • Sasakian manifolds • Statistical manifolds • submanifolds |
| ISBN-10 | 981-96-2818-0 / 9819628180 |
| ISBN-13 | 978-981-96-2818-6 / 9789819628186 |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
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