New PDF release: Contact Manifolds in Riemannian Geometry

By David Ervin Blair (auth.)

ISBN-10: 3540076263

ISBN-13: 9783540076261

ISBN-10: 3540381546

ISBN-13: 9783540381549

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Extra info for Contact Manifolds in Riemannian Geometry

Example text

Thus, of d~ along vanishes an induced speaking m through structure. submanifold space m is V we study restrictive 6 M 2n+l the the g e o m e t r y in C h a p t e r a very at in distribu- an r - d i m e n s i o n a l D due to of a c o n t a c t the S a s a k i a n be a vector < r < n) abundance is again to an integral so l o o s e l y of o n l y Theorem. submanifold m . is that namely 5x i ~u X is one of the d i f f i c u l t i e s is n o r m a l submanifolds Mr(l at submanifolds to the submanifold.

U . Thus, integral a symplectic manifold with fl''''' as c o m p a c t on on vectors. H. denotes the h o r i z o n t a l lift w i t h 46 respect to the connection form d ~ ( X i , X j) = ~ ( X f . , X f ) o ~ l 3 = O and . ] l 3 lifts to a f o l i a t i o n ~ . Then and h e n c e Thus, by ~(X i) = 0 ~([Xi,Xj]) the L a g r a n g i a n integral and = 0 foliation submanifolds of D . CHAPTER IV K-CONTACT AND SASAKIAN i. Normal Almost In C h a p t e r that Contact II we s t u d i e d is m a n i f o l d s with STRUCTURES almost structural these m a n i f o l d s can be ogues of a l m o s t complex manifolds.

HT M TM is i s o m o r p h i c to the m a x i m a l P c o m p l e x s u b s p a c e c o n t a i n e d in T Mm .

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Contact Manifolds in Riemannian Geometry by David Ervin Blair (auth.)


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