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Nearly Pseudo-Kähler Manifolds and Related Special Holonomies 1st ed. 2017 [Minkštas viršelis]

  • Formatas: Paperback / softback, 183 pages, aukštis x plotis: 235x155 mm, weight: 2993 g, VII, 183 p., 1 Paperback / softback
  • Serija: Lecture Notes in Mathematics 2201
  • Išleidimo metai: 15-Sep-2017
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319658069
  • ISBN-13: 9783319658063
Kitos knygos pagal šią temą:
Nearly Pseudo-Kähler Manifolds and Related Special Holonomies 1st ed. 2017Didesnis paveikslėlis
  • Formatas: Paperback / softback, 183 pages, aukštis x plotis: 235x155 mm, weight: 2993 g, VII, 183 p., 1 Paperback / softback
  • Serija: Lecture Notes in Mathematics 2201
  • Išleidimo metai: 15-Sep-2017
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319658069
  • ISBN-13: 9783319658063
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783319658063.html
Raktažodžiai:
Developing and providing an overview of recent results on nearly Kähler geometry on pseudo-Riemannian manifolds, this monograph emphasizes the differences with the classical Riemannian geometry setting. The focal objects of the text are related to special holonomy and Killing spinors and have applications in high energy physics, such as supergravity and string theory. Before starting into the field, a self-contained introduction to the subject is given, aimed at students with a solid background in differential geometry. The book will therefore be accessible to masters and Ph.D. students who are beginning work on nearly Kähler geometry in pseudo-Riemannian signature, and also to non-experts interested in gaining an overview of the subject.  Moreover, a number of results and techniques are provided which will be helpful for differential geometers as well as for high energy physicists interested in the mathematical background of the geometric objects they need.

Recenzijos

This monography contains not only results of the author but also related work of other researchers. It provides detailed motivation described in the introduction, appropriate examples for better understanding of theoretical results, as well as applications in other fields, especially in supergravity and string theories. (Neda Bokan, zbMATH 1380.53004, 2018)

1 Introduction
1(16)
1.1 Stable Forms, Half-Flat Structures and Holonomy
1(2)
1.2 Nearly Kahler Geometry
3(7)
1.3 Special Kahler Manifolds
10(1)
1.4 Summary
11(2)
1.5 Zusammenfassung
13(4)
2 Preliminaries
17(24)
2.1 Stable Forms
17(11)
2.1.1 Real Forms of SL(3, C)
23(2)
2.1.2 Relation Between Real Forms of SL(3, C) and GC2
25(2)
2.1.3 Relation Between Real Forms of G and Spin(7, C)
27(1)
2.2 Almost Pseudo-Hermitian and Almost Para-Hermitian Geometry
28(4)
2.3 Linear Algebra of Three-Forms in Dimension 8 and 10
32(2)
2.4 Structure Reduction of Almost e-Hermitian Six-Manifolds
34(2)
2.5 Pseudo-Riemannian Submersions
36(1)
2.6 Para-Sasaki Manifolds
37(4)
2.6.1 The T-Dual Space
38(3)
3 Nearly Pseudo-Kahler and Nearly Para-Kahler Manifolds
41(90)
3.1 Nearly Pseudo-Kahler and Nearly Para-Kahler Manifolds
41(11)
3.1.1 General Properties
41(4)
3.1.2 Characterisations by Exterior Differential Systems in Dimension 6
45(5)
3.1.3 Curvature Identities for Nearly ε-Kahler Manifolds
50(2)
3.2 Structure Results
52(6)
3.2.1 Kahler Factors and the Structure in Dimension 8
52(1)
3.2.2 Einstein Condition Versus Reducible Holonomy
53(5)
3.3 Twistor Spaces over Quaternionic and Para-Quaternionic Kahler Manifolds
58(4)
3.4 Complex Reducible Nearly Pseudo-Kahler Manifolds
62(10)
3.4.1 General Properties
62(1)
3.4.2 Co-dimension Two
63(1)
3.4.3 Six-Dimensional Nearly Pseudo-Kahler Manifolds
64(2)
3.4.4 General Dimension
66(5)
3.4.5 The Twistor Structure
71(1)
3.5 A Class of Flat Pseudo-Riemannian Lie Groups
72(4)
3.6 Classification Results for Flat Nearly e-Kahler Manifolds
76(8)
3.6.1 Classification Results for Flat Nearly Pseudo-Kahler Manifolds
76(3)
3.6.2 Classification of Flat Nearly Para-Kahler Manifolds
79(5)
3.7 Conical Ricci-Flat Nearly Para-Kahler Manifolds
84(5)
3.8 Evolution of Hypo Structures to Nearly Pseudo-Kahler Six-Manifolds
89(11)
3.8.1 Linear Algebra of Five-Dimensional Reductions of SU(1,2)-Structures
89(2)
3.8.2 Evolution of Hypo Structures
91(4)
3.8.3 Evolution of Nearly Hypo Structures
95(5)
3.9 Results in the Homogeneous Case
100(12)
3.9.1 Consequences for Automorphism Groups
100(2)
3.9.2 Left-Invariant Nearly ε-Kahler Structures On SL(2,R) x SL(2, R)
102(4)
3.9.3 Real Reducible Holonomy
106(1)
3.9.4 3-Symmetric Spaces
106(6)
3.10 Lagrangian Submanifolds in Nearly Pseudo-Kahler Manifolds
112(19)
3.10.1 Definitions and Geometric Identities
113(3)
3.10.2 Lagrangian Submanifolds in Nearly Kahler Six-Manifolds
116(2)
3.10.3 The Splitting Theorem
118(5)
3.10.4 Lagrangian Submanifolds in Twistor Spaces
123(4)
3.10.5 Deformations of Lagrangian Submanifolds in Nearly Kahler Manifolds
127(4)
4 Hitchin's Flow Equations
131(44)
4.1 Half-Flat Structures and Parallel G2(*)-Structures
131(11)
4.1.1 Remark on Completeness: Geodesically Complete Conformal G2-Metrics
136(2)
4.1.2 Nearly Half-Flat Structures and Nearly Parallel G2(*)-Structures
138(2)
4.1.3 Cocalibrated G2(*)-Structures and Parallel Spin(7)- and Spinp(3,4)-Structures
140(2)
4.2 Evolution of Nearly ε-Kahler Manifolds
142(4)
4.2.1 Cones over Nearly ε-Kahler Manifolds
142(2)
4.2.2 Sine Cones over Nearly ε-Kahler Manifolds
144(1)
4.2.3 Cones over Nearly Parallel G2(*)-Structures
145(1)
4.3 The Evolution Equations on Nilmanifolds Γ \ H3 x H3
146(15)
4.3.1 Evolution of Invariant Half-Flat Structures on Nilmanifolds
147(3)
4.3.2 Left-Invariant Half-Flat Structures on H3 x H3
150(7)
4.3.3 Solving the Evolution Equations on H3 x H3
157(4)
4.4 Special Geometry of Real Forms of the Symplectic SL(6, C)-Module ˆ3C6
161(14)
4.4.1 The Symplectic SL(6, C)-Module V = ˆ3C6 and Its Lagrangian Cone C(X) of Highest Weight Vectors
163(1)
4.4.2 Real Forms (G, Vo) of the Complex Module (SL(6.C).V)
163(1)
4.4.3 Classification of Open C-Orbits on the Grassmannian X and Corresponding Special Kahler Manifolds
164(6)
4.4.4 The Homogeneous Projective Special Para-Kahler Manifold SL(6, R)/ S(GL(3, R) x GL(3, R))
170(5)
References 175(6)
Index 181