Symplectic curvature and the arnold form over and isotropic submanifold

1996 ◽  
Vol 82 (6) ◽  
pp. 3789-3799 ◽  
Author(s):  
M. V. Karasev ◽  
Yu. M. Vorobjev
Keyword(s):  
Isotropic Submanifold

scholarly journals TANGENT DIRAC STRUCTURES AND SUBMANIFOLDS

2005 ◽  
Vol 02 (05) ◽  
pp. 759-775 ◽  
Author(s):  
IZU VAISMAN
Keyword(s):  
Poisson Structure ◽  
Normal Bundle ◽  
Dirac Structure ◽  
Dirac Structures ◽  
Isotropic Submanifold ◽  
Coisotropic Submanifold ◽  
Definition Of ◽  
Simple Definition ◽  
The Way

We write down the local equations that characterize the submanifolds N of a Dirac manifold M which have a normal bundle that is either a coisotropic or an isotropic submanifold of TM endowed with the tangent Dirac structure. In the Poisson case, these formulas once again prove a result of Xu: the submanifold N has a normal bundle which is a coisotropic submanifold of TM with the tangent Poisson structure if and only if N is a Dirac submanifold. In the presymplectic case it is the isotropy of the normal bundle which characterizes the corresponding notion of a Dirac submanifold. On the way, we give a simple definition of the tangent Dirac structure, make new remarks about it and establish its characteristic, local formulas for various interesting classes of submanifolds of a Dirac manifold.

scholarly journals Contact co-isotropic CR submanifolds of a pseudo-Sasakian manifold

1984 ◽  
Vol 7 (2) ◽  
pp. 339-350 ◽  
Author(s):  
Vladislav V. Goldberg ◽  
Radu Rosca
Keyword(s):  
Vertical Distribution ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Totally Geodesic ◽  
Isotropic Submanifold ◽  
Cr Submanifold ◽  
Necessary And Sufficient ◽  
Cr Submanifolds

It is proved that any co-isotropic submanifoldMof a pseudo-Sasakian manifoldM˜(U,ξ,η˜,g˜)is a CR submanifold (such submanfolds are called CICR submanifolds) with involutive vertical distributionν1. The leavesM1ofD1are isotropic andMisν1-totally geodesic. IfMis foliate, thenMis almost minimal. IfMis RicciD1-exterior recurrent, thenMreceives two contact Lagrangian foliations. The necessary and sufficient conditions forMto be totally minimal is thatMbe contactD1-exterior recurrent.

scholarly journals Symplectic hypersurfaces in the complement of an isotropic submanifold

2001 ◽  
Vol 321 (4) ◽  
pp. 739-754 ◽  
Author(s):  
Denis Auroux ◽  
Damien Gayet ◽  
Jean-Paul Mohsen
Keyword(s):  
Isotropic Submanifold
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