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Sorin Dragomir, Liviu Ornea, "Locally Conformal Kahler Geometry"

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.

This is a unique monograph covering topics in complex geometry, an area of mathematical growth in recent years. The latest topics are addressed systematically, bringing us to the cutting edge in the mathematics of locally conformal Kahler (I.c.K.) manifold theory.

Locally Confionnal hiihrlerGeomety is a differential geometric study of l.c.K. manifolds (i.e., manifolds carrying some l.c.K. metric) and their submanifolds. While the latest results on Vaisman's conjectures, spectral geometry of generalized Hopf manifolds. harmonic and holomorphic forms of l.c.K. manifolds, and pseudoharmonic maps or Hermitian surfaces are

reviewed throughout the mathematics literature, here they are presented in a systematic manner, and many specific examples (e.g., complex Hopf manifolds, Inoue surfaces, and Thurston's manifolds) are discussed from this wider perspective.

The accent in submanifold theory is on the modern results on Cauchy-Riemann (CR) submanifolds of I.c.K. manifolds, for example, the classification of extrinsic spheres of a generalized Hopf manifold, the classification of compact minimal CR submanifolds, generically embedded in a complex Hopf manifold with the Boothby metric. This monograph explores the interrelation between l.c.K. metrics and other intensely studied geometric objects. such as Sasakian metrics, cosymplectic and locally conformal cosymplectic structures. f-structures, Chen's class, geodesic symmetries, and Kobayashi's submersed CR submanifolds.

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