HOLOMORPHIC FLOWS WITH PERIODIC ORBITS ON STEIN SURFACES

J−holomorphic Curves and Periodic Reeb Orbits *

We study the J−holomorphic curves in the symplectization of the contact manifolds and prove that there exists at least one periodic Reeb orbits in any closed contact manifold with any contact form by using the well-known Gromov's nonlinear Fredholm alternative for J−holomorphic curves. As a corollary, we give a complete solution on the well-known Weinstein conjecture.

Holomorphic fiber bundle with Stein base and Stein fibers

A surjective holomorphic map Π : X → Y between complex spaces is said to be a Stein morphism, if for every point y ∈ Y , there exists an open neighborhood U of y such that Π(U) is Stein. In 1977, Skoda [12] showed that a locally trivial analytic fiber bundle Π : X → Ω with Stein base and Stein fibers is not necessarily a Stein manifold. Thus giving a negative answer to a conjecture proposed in ...

Periodic Orbits of Weakly Exact Magnetic Flows

For a weakly exact magnetic flows with a bounded primitive on a closed Riemannian manifold, we prove the existence of periodic orbits in almost all energy levels below of the Mañé’s critical value. Mathematics Subject Classification: 37J45

Periodic Orbits and Holonomy for Hyperbolic Flows

[14]. More precisely, we have this error term if we can choose three closed orbits of least periods l1, l2, l3 such that θ = (l1 − l2)/(l2 − l3) is diophantine, i.e., there exists C > 0 and β > 0 such that |qθ − p| ≥ Cq−(1+β) for all p ∈ Z and q ∈ N. In this paper we shall consider compact groups extensions of hyperbolic flows. Let G be a compact Lie group. Let φ̂t : Λ̂ → Λ̂ be a topologically wea...

Holomorphic Submersions from Stein Manifolds