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AuthorDragomir, Sorin. author
TitleLocally Conformal Kรคhler Geometry [electronic resource] / by Sorin Dragomir, Liviu Ornea
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1998
Connect tohttp://dx.doi.org/10.1007/978-1-4612-2026-8
Descript XIII, 330 p. online resource

SUMMARY

. E C, 0 < 1>'1 < 1, and n E Z, n ̃ 2. Let̃.>. be the O-dimensional Lie n group generated by the transformation z ̃ >.z, z E C - {a}. Then (cf


CONTENT

1 L.c.K. Manifolds -- 2 Principally Important Properties -- 2.1 Vaismanโ{128}{153}s conjectures -- 2.2 Reducible manifolds -- 2.3 Curvature properties -- 2.4 Blow-up -- 2.5 An adapted cohomology -- 3 Examples -- 3.1 Hopf manifolds -- 3.2 The Inoue surfaces -- 3.3 A generalization of Thurstonโ{128}{153}s manifold -- 3.4 A four-dimensional solvmanifold -- 3.5 SU(2) x S1 -- 3.6 Noncompact examples -- 3.7 Brieskorn & Van de Venโ{128}{153}s manifolds -- 4 Generalized Hopf manifolds -- 5 Distributions on a g.H. manifold -- 6 Structure theorems -- 6.1 Regular Vaisman manifolds -- 6.2 L.c.K.0 manifolds -- 6.3 A spectral characterization -- 6.4 k-Vaisman manifolds -- 7 Harmonic and holomorphic forms -- 7.1 Harmonic forms -- 7.2 Holomorphic vector fields -- 8 Hermitian surfaces -- 9 Holomorphic maps -- 9.1 General properties -- 9.2 Pseudoharmonic maps -- 9.3 A Schwarz lemma -- 10 L.c.K. submersions -- 10.1 Submersions from CH?n -- 10.2 L.c.K. submersions -- 10.3 Compact total space -- 10.4 Total space a g.H. manifold -- 11 L.c. hyperKรคhler manifolds -- 12 Submanifolds -- 12.1 Fundamental tensors -- 12.2 Complex and CR submanifolds -- 12.3 Anti-invariant submanifolds -- 12.4 Examples -- 12.5 Distributions on submanifolds -- 12.6 Totally umbilical submanifolds -- 13 Extrinsic spheres -- 13.1 Curvature-invariant submanifolds -- 13.2 Extrinsic and standard spheres -- 13.3 Complete intersections -- 13.4 Yanoโ{128}{153}s integral formula -- 14 Real hypersurfaces -- 14.1 Principal curvatures -- 14.2 Quasi-Einstein hypersurfaces -- 14.3 Homogeneous hypersurfaces -- 14.4 Type numbers -- 14.5 L. c. cosymplectic metrics -- 15 Complex submanifolds -- 15.1 Quasi-Einstein submanifolds -- 15.2 The normal bundle -- 15.3 L.c.K. and Kรคhler submanifolds -- 15.4 A Frankel type theorem -- 15.5 Planar geodesic immersions -- 16 Integral formulae -- 16.1 Hopf fibrations -- 16.2 The horizontal lifting technique -- 16.3 The main result -- 17 Miscellanea -- 17.1 Parallel IInd fundamental form -- 17.2 Stability -- 17.3 f-Structures -- 17.4 Parallel f-structure P -- 17.5 Sectional curvature -- 17.6 L. c. cosymplectic structures -- 17.7 Chenโ{128}{153}s class -- 17.8 Geodesic symmetries -- 17.9 Submersed CR submanifolds -- A Boothby-Wang fibrations -- B Riemannian submersions


Mathematics Geometry Differential geometry Mathematics Differential Geometry Geometry



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