Infinitesimal characterization of almost Hermitian homogeneous spaces
نویسندگان
چکیده
In this note it is shown that almost Hermitian locally homogeneous manifolds are determined, up to local isometries, by an integer kH , the covariant derivatives of the curvature tensor up to order kH + 2 and the covariant derivatives of the complex structure up to the second order calculated at some point. An example of a Hermitian locally homogeneous manifold which is not locally isometric to any Hermitian globally homogeneous manifold is given.
منابع مشابه
Homogeneous holomorphic hermitian principal bundles over hermitian symmetric spaces
We give a complete characterization of invariant integrable complex structures on principal bundles defined over hermitian symmetric spaces, using the Jordan algebraic approach for the curvature computations. In view of possible generalizations, the general setup of invariant holomorphic principal fibre bundles is described in a systematic way.
متن کاملAlmost power-Hermitian rings
In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.
متن کاملHermitian metric on quantum spheres
The paper deal with non-commutative geometry. The notion of quantumspheres was introduced by podles. Here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.
متن کاملCoupled Vortex Equations and Moduli: Deformation Theoretic Approach and Kähler Geometry
We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kähler manifold X . These solutions are known to be related to polystable triples via a Kobayashi–Hitchin type correspondence. Using a characterization of infinitesimal deformations in terms of the cohomology of a certain elliptic double complex, we construct a Hermi...
متن کامل