Locally Conformal Kähler Geometry

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

Inhalt

-3c2.- 10.2.2 An almost Hermitian submersion with total space R2n-1(c) x R.- 10.2.3 An almost Hermitian submersion with total space (R x Bn-1)(c, k) x R, k < -3c2.- 10.3 Compact total space.- 10.4 Total space a g.H. manifold.- 11 L.c. hyperKähler 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 Yano'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 Kähler 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 Chen's class.- 17.8 Geodesic symmetries.- 17.9 Submersed CR submanifolds.- A Boothby-Wang fibrations.- B Riemannian submersions.