Proper holomorphic Legendrian curves in SL2(C)
نویسنده
چکیده
In this paper we prove that every open Riemann surface properly embeds in the Special Linear group SL2(C) as a holomorphic Legendrian curve, where SL2(C) is endowed with its standard contact structure. As a consequence, we derive the existence of proper, weakly complete, flat fronts in the real hyperbolic space H with arbitrary complex structure.
منابع مشابه
THE CONTACT HOMOLOGY OF LEGENDRIAN SUBMANIFOLDS IN R2n+1
We define the contact homology for Legendrian submanifolds in standard contact (2n + 1)-space using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex n-space. This homology provides new invariants of Legendrian isotopy which indicate that the theory of Legendrian isotopy is very rich. Indeed, in [4] the homology is used to detect infinite families of pairwise non...
متن کاملGenerating function polynomials for legendrian links
It is shown that, in the 1{jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component of the links considered is legendrian isotopic to the 1{jet of the 0{function, and thus cannot be distinguished by the classical rotation number or Thurston{Bennequin invariants. The links are distin...
متن کاملSpecial Legendrian submanifolds in toric Sasaki–Einstein manifolds
We show every toric Sasaki–Einstein manifold S admits a special Legendrian submanifold L which arises as the link fix(τ) ∩ S of the fixed point set fix(τ) of an anti-holomorphic involution τ on the cone C(S). In particular, we obtain a special Legendrian torus S × S in an irregular toric Sasaki–Einstein manifold which is diffeomorphic to S × S. Moreover, there exists a special Legendrian subman...
متن کامل2 8 D ec 2 00 4 INVARIANTS OF KNOTS , EMBEDDINGS AND IMMERSIONS VIA CONTACT GEOMETRY
This paper is an overview of the idea of using contact geometry to construct invariants of immersions and embeddings. In particular, it discusses how to associate a contact manifold to any manifold and a Legendrian submanifold to an embedding or immersion. We then discuss recent work that creates invariants of immersions and embeddings using the Legendrian contact homology of the associated Leg...
متن کاملInvariants of Knots, Embeddings and Immersions via Contact Geometry
This paper is an overview of the idea of using contact geometry to construct invariants of immersions and embeddings. In particular, it discusses how to associate a contact manifold to any manifold and a Legendrian submanifold to an embedding or immersion. We then discuss recent work that creates invariants of immersions and embeddings using the Legendrian contact homology of the associated Leg...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016