Geometry of CR-submanifolds

Aurel Bejancu


  • I: Differential-Geometrical Structures on Manifolds.- 1. Linear connections on a manifold.- 2. The Levi-Civita connection.- 3. Submanifolds of a Riemannian manifold.- 4. Distributions on a manifold.- 5. Kaehlerian manifolds.- 6. Sasakian manifolds.- 7. Quaternion Kaehlerian manifolds.- II: CR-Submanifolds of Almost Hermitian Manifolds.- 1. CR-submanifolds and CR-structures.- 2. Integrability of distributions on a CR-submanifold.- 3. ?-connections on a CR-submanifold and CR-products of almost Hermitian manifolds.- 4. The non-existence of CR-products in S6.- III: CR-Submanifolds of Kaehlerian Manifolds.- 1. Integrability of distributions and geometry of leaves.- 2. Umbilical CR-submanifolds of Kaehlerian manifolds.- 3. Normal CR-submanifolds of Kaehlerian manifolds.- 4. Normal anti-holomorphic submanif olds of Kaehlerian manifolds.- 5. CR-products in Kaehlerian manifolds.- 6. Sasakian anti-holomorphic submanifolds of Kaehlerian manifolds.- 7. Cohomology of CR-submanifolds.- IV: CR-Submanifolds of Complex Space Forms.- 1. Characterization of CR-submanifolds in complex space forms.- 2. Riemannian fibre bundles and anti-holomorphic submanifolds of CPn.- 3. CR-products of complex space forms.- 4. Mixed foliate CR-submanifolds of complex space forms.- 5. CR-submanifolds with semi-flat normal connection.- 6. Pinching theorems for sectional curvatures of CR-submanifolds.- V: Extensions of CR-Structures to Other Geometrical Structures.- 1. Semi-invariant submanifolds of Sasakian manifolds.- 2. Semi-invariant products of Sasakian manifolds.- 3. Semi-invariant submanifolds with flat normal connection.- 4. Generic submanifolds of Kaehlerian manifolds.- 5. QR-submanifolds of quaternion Kaehlerian manifolds.- 6. Totally umbilical and toally geodesic QR-submanifolds of quaternion Kaehlerian manifolds.- VI: CR-Structures and Pseudo-Conformal Mappings.- 1. CR-manifolds and f-structures with complemented frames.- 2. Generic submanifolds of complex manifolds.- 3. Anti-holomorphic submanifolds of complex manifolds.- 4. Pseudo-conformal mappings.- VII: CR-Structures and Relativity.- 1. Geometrical Structures of space-time.- 2. The twistor space and Penrose correspondence.- 3. Physical interpretations of CR-structures.- References.- Author Index.

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書名 Geometry of CR-submanifolds
著作者等 Bejancu, Aurel
シリーズ名 Mathematics and its applications
出版元 D. Reidel Pub. Co.
Sold and Kluwer Academic
刊行年月 c1986
ページ数 xii, 169 p.
大きさ 23 cm
ISBN 9027721947
NCID BA01214058
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言語 英語
出版国 オランダ