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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Kodai Mathematical Journal
( Vol. 29 NO.3 / (2006))
Jacobi fields of the Tanaka-Webster connection on Sasakian manifolds
Elisabetta Barletta, Sorin Dragomir,
Pages. 406-454
Abstract We build a variational theory of geodesics of the Tanaka-Webster
connection $
abla$ on a strictly pseudoconvex CR manifold $M$.
Given a contact form $ heta$ on $M$ such that $(M, heta)$ has
nonpositive pseudohermitian sectional curvature $(k_ heta(sigma)
leq 0)$ we show that $(M, heta)$ has no horizontally conjugate
points. Moreover, if $(M, heta)$ is a Sasakian manifold such that
$k_ heta(sigma)leq k_0 > 0$ then we show that the distance
between any two consecutive conjugate points on a lengthy geodesic
of $
abla$ is at most $pi/(2 sqrt{k_0})$. We obtain the first and
second variation formulae for the Riemannian length of a curve in $M$
and show that in general geodesics of $
abla$ admitting horizontally
conjugate points do not realize the Riemannian distance.
Contents 1. Introduction
2. Sub-Riemannian geometry on CR manifolds
3. Jacobi fileds on CR manifolds
4. CR manifolds without conjugate points
5. Jacobi fields on CR manifolds of constant pseudohermitian sectional curvature
6. Conjugate points on Sasakian manifolds
7. The first variation of the length integral
8. The second variation of the length integral
9. Final comments and open problems
Key words
Mathmatical Subject Classification