Conformal Vector Fields, Ricci Solitons and Related Topics (Infosys Science Foundation Series)

Preface
Contents
1 Manifolds and Submanifolds Reviewed
	1.1 Differentiable Manifolds
	1.2 Vector and Tensor Fields
	1.3 Covariant and Exterior Derivatives
	1.4 Semi-Riemannian Manifolds
	1.5 Submanifolds and Hypersurfaces
	References
2 Lie Group and Lie Derivative
	2.1 Lie Group and Lie Algebra
	2.2 Lie Derivative
	2.3 Properties of Lie Derivative
	2.4 Computation of Lie Derivatives
	2.5 Commutation Formulas for Lie and Covariant Derivatives
	References
3 Conformal Transformations
	3.1 Conformal Transformation
	3.2 Conformal Transformations of Geometric Objects
	3.3 Other Tensors Related to Weyl and Ricci Tensors
	3.4 Isometries and Killing Vector Fields
	References
4 Conformal Vector Fields
	4.1 Conformal Vector Fields
	4.2 Zeros of Conformal Vector Fields
	4.3 Zeros of Conformal Vector Fields on Semi-Riemannian Manifolds
	4.4 Essential Conformal Vector Fields
	4.5 Lichnerowicz Conjecture in CR Geometry
	References
5 Integral Formulas and Conformal Vector Fields
	5.1 Integration Theorems
	5.2 Integral Formulas
	5.3 Some Classical Results on Conformal Vector Fields
	5.4 More Results on Conformal Vector Fields
	References
6 Conformal Vector Fields on Lorentzian Manifolds
	6.1 Space-Times and Kinematics
	6.2 Einstein\'s Field Equations
	6.3 Some Important Space-Times
	6.4 Homothetic Vector Fields in General Relativity
	6.5 Homothetic Symmetry and Cauchy Surfaces
	6.6 Conformal Vector Fields on Space-Times
	6.7 Inheriting Conformal Vector Fields
	References
7 Ricci Solitons
	7.1 Preliminaries
	7.2 Ricci Flow
	7.3 Ricci Soliton
	7.4 Some Results on Ricci Solitons
	References
8 Conformal Vector Fields and Ricci Solitons in Complex and Contact Geometries
	8.1 Complex and Almost Complex Manifolds
	8.2 Contact Manifolds
	8.3 Conformal Vector Fields on Almost Hermitian Manifolds
	8.4 Conformal Vector Fields on Contact Metric Manifolds
	8.5 Kähler–Ricci Solitons
	8.6 Contact Metrics as Ricci Solitons
	References
9 Ricci Almost Solitons and Generalized Quasi-Einstein Manifolds
	9.1 Ricci Almost Solitons
	9.2 Generalized Quasi-Einstein Manifolds
	9.3 Generalized m-Quasi-Einstein Manifolds with Conformal Vector Fields
	9.4 Generalized m-Quasi-Einstein Manifolds in Contact Geometry
	References
10 Yamabe Solitons
	10.1 Yamabe Problem
	10.2 Yamabe Flow and Yamabe Solitons
	10.3 Conformal Solutions of Yamabe Flow
	10.4 Yamabe Solitons in Contact Geometry
	10.5 Concluding Remarks
	References
Index