Some sufficient and necessary conditions were given for integrabilities of distribution D｛ξ｝ on a nearly Sasakian manifold,and generalized Bejancu's result was given also.

In this paper, we rstly study dierentiable functions on M, where M is a pseudo-umbilical CR-submanifold of an almost Hermitian manifold, then give a theorem which concern about geodesic character of M, and extend Bejancu and Chen B.Y.'s conclusions.

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Integrabilities of distribution D｛ξ｝on a nearly Sasakian manifold

Pseudo-umbilical CR-submanifold of an Almost Hermitian Manifold

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

background

Geometry of CR-submanifolds

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Integrabilities of distribution D｛ξ｝on a nearly Sasakian manifold

Citations

Pseudo-umbilical CR-submanifold of an Almost Hermitian Manifold

References

Geometry of CR-submanifolds

Invariant submanifolds of an almost contact manifold

Pseudo-umbilical CR-submanifold of an Almost Hermitian Manifold

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