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BK

2nd ed.

New York : Birkhäuser, 2010

xv, 343 s. : il. ; 24 cm

ISBN 978-0-8176-4958-6 (váz.)

Progress in mathematics ; vol. 203

Obsahuje bibliografické odkazy a rejstříky

000195589

Contents // Preface to Second Edition vu // Preface to the First Edition ix // 1 Symplectic Manifolds 1 // 1.1 Definitions and examples... 1 // 1.2 Lagrangian submanifolds... 6 // 1.3 The Darboux-Weinstein theorems ... 9 // 1.4 Symplectomorphisms... H // 2 Principal S’1-bundles 15 // 2.1 The set of principal  -bundles as a group... 15 // 2.2 Connections on a principal bundle... 19 // 3 Contact Manifolds 23 // 3.1 Definitions... 23 // 3.2 Examples...  // 3.2.1 K2n+1... 27 // 3.2.2 lRn+1 x PW1 ... 28 // 3.2.3 M2n+1 C K2n+2 with TmM2n+1 ? {0} = 0... 28 // 3.2.4 Unit and projectivized tangent and cotangent // bundles... 29 // 3.2.5 T*M x ... 30 // xii Contents // 3.2.6 Tori... // 3.2.7 Overtwisted contact structures // 3.2.8 S’2 x S1... // 3.2.9 Contact circles... // 3.3 The Boothby-Wang fibration ... // 3.4 The Weinstein conjecture... // 30 // 32 // 34 // 35 // 36 38 // 4 Associated Metrics 41 // 4.1 Almost complex and almost contact structures... 41 // 4.2 Polarization and associated metrics... 45 // 4.3 Polarization of metrics as a projection... 49 // 4.3.1 Some linear algebra ... 50 // 4.3.2 Results on the set A... 53 // 4.4 Action of symplectic and contact transformations... 57 // 4.5 Examples of almost contact metric manifolds... 60 // 4.5.1 K2n+1... 60 // 4.5.2 M2n+1 C M2n+2 almost complex... 61 // 4.5.3 S5CS6...63 // 4.5.4 The Boothby-Wang fibration... 64 // 4.5.5 M2n x ? ... 66 // 4.5.6 Parallelizable manifolds... 67 // 5 Integral Submanifolds and Contact Transformations

// 5.1 Integral submanifolds ... // 5.2 Contact transformations... // 5.3 Examples of integral submanifolds... // 5.3.1 Sn C 52n+1... // 5.3.2 T2CS5... // 5.3.3 Legendre curves and Whitney spheres... // 5.3.4 Lift of a Lagrangian foliation, Legendre foliations // 69 // 69 // 71 // 74 // 74 // 74 // 75 77 // 6 Sasakian and Cosymplectic Manifolds // 6.1 Normal almost contact structures... // 6.2 The tensor field h... // 6.3 Definition of a Sasakian manifold... // 6.4 CR-manifolds... // 6.5 Cosymplectic manifolds and remarks on the Sasakian // definition... // 6.6 Products of almost contact manifolds... // 79 // 79 // 83 // 86 // 89 // 95 // 97 // Contents xiii // 6.7 // 6.8 // Examples... // 6.7.1 R2n+1... // 6.7.2 Principal circle bundles... // 6.7.3 A nonnormal almost contact structure on S° // 6.7.4 M2n+1 C M2n+2... // 6.7.5 Brieskorn manifolds... // Some early topology... // . 100 . 100 . 100 . 102 . 104 . 104 . 106 // 7 // Curvature of Contact Metric Manifolds // 7.1 Basic curvature properties... // 7.2 Curvature of contact metric manifolds . . . // 7.3 The (?, /u)-manifolds... // 7.4 Sasakian Einstein manifolds... // 7.5 Locally symmetric contact metric manifolds // 7.6 Conformally flat contact metric manifolds . // 7.7 (/»-sectional curvature... // 7.8 Examples of Sasakian space forms ... // 7.8.1 // 7.8.2 // 7.8.3 //  2n-fl // K2n+1 // Bn x ] // 7.9 Locally (/»-symmetric spaces // 111 // . Ill . 116 . 123 . 130 . 132 . 133 . 137 . 141 . 142 . 142 . 142 . 143 // 8 Submanifolds

of Kahler and Sasakian Manifolds // 8.1 Invariant submanifolds... // 8.2 Lagrangian and integral submanifolds... // 151 // 151 // 155 // 9 // Tangent Bundles and Tangent Sphere Bundles 169 . 169 // Q 9 . 175 // n Q . 183 // ? .o Q A vjrGOIIlcLI? Ul VcclAJi . 186 // ?.2* 9.5 The geodesic flow on the projectivized tangent bundle . 191 // 10 Curvature Functionals on Spaces of Associated Metrics 195 // 10.1 Introduction to critical metric problems // 10.2 The *-scalar curvature... // 10.3 The integral of Ric(Ł,)... // 10.3.1 H-contact manifolds... // 10.4 The Webster scalar curvature... // 195 // 201 // 206 // 211 // 212 // XIV // Contents // 10.5 A gauge invariant...215 // 10.6 The Abbena metric as a critical point...217 // 11 Negative  -sectional Curvature 219 // 11.1 Special directions in the contact subbundle...219 // 11.2 Anosov flows... 221 // 11.3 Conformally Anosov flows...227 // 12 Complex Contact Manifolds 233 // 12.1 Complex contact manifolds and associated metrics ... 233 // 12.2 Examples of complex contact manifolds...238 // 12.2.1 Complex Heisenberg group ...238 // 12.2.2 Odd-dimensional complex projective space...240 // 12.2.3 Twistor spaces...242 // 12.2.4 The Complex Boothby-Wang fibration...244 // 12.2.5 3-dimensional homogeneous examples ...- 246 // 12.2.6 Complex contact Lie groups...247 // 12.2.7 Cn+1 x CPn(16)...248 // 12.2.8 cos z3dz1 + sin z3dz2...250 // 12.3 Normality of complex contact manifolds...250 // 12.4 GP-sectional curvature ...252 // 12.5 The set

of associated metrics and integral functionals ... 255 // 12.6 Holomorphic Legendre curves...257 // 12.7 The Calabi (Veronese) embeddings as integral // submanifolds of CP2n+1...260 // 13 Additional Topics in Complex Geometry 265 // 13.1 Partial and holomorphic hyperbolicity...265 // 13.2 Projectivized holomorphic bundles...268 // 13.3 The complex geodesic flow...271 // 13.4 Complex almost contact metric structure on Pr...278 // 13.4.1 A complex contact structure with nonintegrable // vertical subbundle...280 // 13.5 Special directions on complex contact manifolds and the // Lie group 5L(2,C)...283 // 14 3-Sasakian Manifolds // 14.1 3-Sasakian manifolds // 14.2 Integral submanifolds // Erratum Bibliography Subject Index Author Index // Contents XV // 291 // ...291 // ...299 // El // 303 // 335 // 339