Covers topics in complex geometry, focusing on the locally conformal Kahler(l.c.K.) theory. Explores the interrelation between l.c.K metrics and Sasakian metrics, f-structures, Chen's class and geodesic symmetries. DLC: Kahlerin manifolds.
Author(s): Sorin Dragomir, Liuiu Ornea
Series: Progress in Mathematics
Publisher: Birkhauser
Year: 1998
Language: English
Pages: 346
Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents......Page 6
Dedication......Page 9
Introduction......Page 10
1 L.c.K. Manifolds......Page 16
2.1 Vaisman's conjectures......Page 22
2.2 Reducible manifolds......Page 25
2.3 Curvature properties......Page 26
2.4 Blow-up......Page 30
2.5 An adapted cohomology......Page 31
3.1 Hopf manifolds......Page 36
3.2 The Inoue surfaces......Page 38
3.3 A generalization of Thurston's manifold......Page 40
3.4 A four-dimensional solvmanifold......Page 41
3.6 Noncompact examples......Page 43
3.7 Brieskorn & Van de Ven's manifolds......Page 44
4 Generalized Hopf manifolds......Page 48
5 Distributions on a g.H. manifold......Page 56
6.1 Regular Vaisman manifolds......Page 64
6.2 L.c.K.0 manifolds......Page 71
6.3 A spectral characterization......Page 75
6.4 k-Vaisman manifolds......Page 81
7.1 Harmonic forms......Page 84
7.2 Holomorphic vector fields......Page 94
8 Hermitian surfaces......Page 100
9.1 General properties......Page 118
9.2 Pseudoharmonic maps......Page 122
9.3 A Schwarz lemma......Page 126
10.1 Submersions from CH'......Page 136
10.2 L.c.K. submersions......Page 139
10.2.1 An almost Hermitian submersion with total space Stn-1(c, k) x R, k > -3c2......Page 140
10.2.2 An almost Hermitian submersion with total space R211-1(c) x R......Page 141
10.2.3 An almost Hermitian submersion with total space (R x Bn-1)(c,k) x R, k < -3c2......Page 142
10.3 Compact total space......Page 143
10.4 Total space a g.H. manifold......Page 145
11 L.c. hyperKahler manifolds......Page 148
12.1 Fundamental tensors......Page 162
12.2 Complex and CR submanifolds......Page 168
12.3 Anti-invariant submanifolds......Page 173
12.4 Examples......Page 179
12.5 Distributions on submanifolds......Page 182
12.6 Totally umbilical submanifolds......Page 187
13.1 Curvature-invariant submanifolds......Page 202
13.2 Extrinsic and standard spheres......Page 209
13.3 Complete intersections......Page 217
13.4 Yano's integral formula......Page 227
14.1 Principal curvatures......Page 234
14.2 Quasi-Einstein hypersurfaces......Page 238
14.3 Homogeneous hypersurfaces......Page 240
14.4 Type numbers......Page 241
14.5 L. c. cosymplectic metrics......Page 247
15.1 Quasi-Einstein submanifolds......Page 254
15.2 The normal bundle......Page 259
15.3 L.c.K. and Kahler submanifolds......Page 266
15.4 A F4ankel type theorem......Page 268
15.5 Planar geodesic immersions......Page 270
16.1 Hopf fibrations......Page 272
16.2 The horizontal lifting technique......Page 275
16.3 The main result......Page 282
17.1 Parallel Ilnd fundamental form......Page 290
17.2 Stability......Page 292
17.3 f -Structures......Page 293
17.4 Parallel f -structure P......Page 298
17.5 Sectional curvature......Page 300
17.6 L. c. cosymplectic structures......Page 301
17.7 Chen's class......Page 304
17.8 Geodesic symmetries......Page 306
17.9 Submersed CR submanifolds......Page 307
A Boothby-Wang fibrations......Page 314
B Riemannian submersions......Page 318
Bibliography......Page 322
Back Cover......Page 346
