Geometric connections and geometric Dirac operators on contact manifolds
نویسندگان
چکیده
منابع مشابه
Geometric connections and geometric Dirac operators on contact manifolds
We construct some natural metric connections on metric contact manifolds compatible with the contact structure and characterized by the Dirac operators they determine. In the case of CR manifolds these are invariants of a fixed pseudo-hermitian structure, and one of them coincides with the Tanaka–Webster connection. 2005 Elsevier B.V. All rights reserved. MSC: 53B05; 53C15; 53D10; 53D15
متن کاملOn the definition of geometric Dirac operators
For the definition of a spin structure and its associated Dirac operators there can be found two different approaches in the literature. One of them uses lifts of the orthonormal frame bundle to principal spin bundles (cf. [Gil], [GH], [Frie] or [LM]) and the other one irreducible representations of the complex Clifford bundle (cf. [BD] or [Kar1,2]). The first approach is an offspring of vector...
متن کاملDirac Operators on 4-manifolds
Dirac operators are important geometric operators on a manifold. The Dirac operator DA on the four dimensional Euclidean space M = R is the order one differential operator whose square DA ◦ DA is the Euclidean Laplacian − ∑4 i=1 ∂ψ ∂xi . However, this is not possible unless we allow coefficients for this linear operator to be matrix-valued. Let M = R be the four dimensional Euclidean space with...
متن کاملAnalysis of Geometric Operators on Open Manifolds: a Groupoid Approach
The first five sections of this paper are a survey of algebras of pseudodifferential operators on groupoids. We thus review differentiable groupoids, the definition of pseudodifferential operators on groupoids, and some of their properties. We use then this background material to establish a few new results on these algebras that are useful for the analysis of geometric operators on non-compact...
متن کاملSome remarks on the geometric quantization of contact manifolds
Suppose that (M,E) is a compact contact manifold, and that a compact Lie group G acts on M transverse to the contact distribution E. In [14], we defined a G-transversally elliptic Dirac operator Db / , constructed using a Hermitian metric h and connection ∇ on the symplectic vector bundle E → M , whose equivariant index is well-defined as a generalized function on G, and gave a formula for its ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2005
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2005.03.008