Riemannian Submersions and Related Topics

by Falcitelli, Maria; Pastore, Anna Maria; Ianus, Stere

• ISBN13: 9789812388964
• ISBN10: 9812388966
• Format: Hardcover
• Copyright: 2004-06-21
• Publisher: Textstream

Summary

- First systematic exposition devoted to Riemannian submersions- Deals with current material- Contains a wide-ranging bibliography and about 350 references

Table of Contents

Preface	vii
1. Riemannian Submersions	1	(32)
1.1 Riemannian Submersions	2	(2)
1.2 The Hopf Fibration	4	(4)
1.3 Fundamental Tensors and Fundamental Equations	8	(9)
1.4 Other Examples	17	(8)
1.5 Geodesics and O'Neill Theorem	25	(3)
1.6 Clairaut Submersions	28	(5)
2. Submersions with Totally Geodesic Fibres	33	(26)
2.1 Riemannian Submersions with Complete Total Space	34	(4)
2.2 Submersions with Totally Geodesic Fibres	38	(6)
2.3 Riemannian Submersions from the Spheres	44	(5)
2.4 The Uniqueness Theorem	49	(5)
2.5 Submersions from the Complex Projective Spaces	54	(5)
3. Almost Hermitian Submersions	59	(44)
3.1 Almost Hermitian Manifolds	60	(4)
3.2 Almost Hermitian Submersions	64	(7)
3.3 Holomorphic Distributions in Kähler Submersions	71	(4)
3.4 Curvature Properties	75	(6)
3.5 Locally Conformal Kähler Manifolds	81	(7)
3.6 Locally Conformal Kähler Submersions	88	(3)
3.7 Submersions from Generalized Hopf Manifolds	91	(6)
3.8 Almost Complex Conformal Submersions	97	(6)
4. Riemannian Submersions and Contact Metric Manifolds	103	(40)
4.1 Remarkable Classes of Contact Metric Manifolds	104	(5)
4.2 Contact Riemannian Submersions	109	(5)
4.3 Contact-complex Riemannian Submersions	114	(2)
4.4 Complex-contact Riemannian Submersions	116	(4)
4.5 Curvature Properties	120	(2)
4.6 Riemannian Submersions Involving Quaternionic Kähler and 3-Sasakian Manifolds	122	(7)
4.7 Regular f -structures and Riemannian Submersions	129	(14)
5. Einstein Spaces and Riemannian Submersions	143	(52)
5.1 Einstein Metrics on the Total Space of a Riemannian Submersion	144	(4)
5.2 The Canonical Variation of the Metric in the Total Space	148	(5)
5.3 Homogeneous Einstein Spaces	153	(9)
5.4 Einstein Metrics on Principal Bundles	162	(13)
5.5 Einstein Weyl Structures on Principal Bundles	175	(7)
5.6 Einstein Weyl Structures on Hermitian and Sasakian Manifolds	182	(13)
6. Riemannian Submersions and Submanifolds	195	(20)
6.1 Submersions of CR-submanifolds	196	(5)
6.2 Links Between Submanifolds of Sasakian and Kähler Manifolds	201	(8)
6.3 Riemannian Submersions and Isometric Reflections with Respect to the Fibres	209	(6)
7. Semi-Riemannian Submersions	215	(24)
7.1 Semi-Riemannian Manifolds	216	(2)
7.2 Semi-Riemannian Submersions. Examples	218	(3)
7.3 Lorentzian Submersions	221	(2)
7.4 Submersions from Pseudo-hyperbolic Spaces	223	(9)
7.5 Submersions with Totally Umbilical Fibres	232	(4)
7.6 Semi-Riemannian Submersions with Minimal Fibres	236	(3)
8. Applications of Riemannian Submersions in Physics	239	(18)
8.1 Gauge Fields, Instantons and Riemannian Submersions	239	(4)
8.2 Einstein Equations and Kaluza-Klein Ansatz	243	(3)
8.3 Generalized Nonlinear Sigma Model in Curved Space	246	(4)
8.4 Horizontally Conformal Submersions and Gravity	250	(1)
8.5 The Dirac Monopole and the Hopf Map	251	(4)
8.6 Kaluza-Klein Monopole and Taub-NUT Instanton	255	(2)
Bibliography	257	(18)
Index	275