Almost Kähler 4-dimensional Lie Groups with J-invariant Ricci Tensor
نویسنده
چکیده
The aim of this paper is to determine left-invariant strictly almost Kähler structures on 4-dimensional Lie groups (g, J,Ω) such that the Ricci tensor is J-invariant.
منابع مشابه
Einstein structures on four-dimensional nutral Lie groups
When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...
متن کاملA Remark on Ricci Flow of Left Invariant Metrics
We prove that the Ricci flow equation for left invariant metrics on Lie groups reduces to a first order ordinary differential equation for a map Q : (−a, a) → UT , where UT is the group of upper triangular matrices. We decompose the matrix Rij of Ricci tensor coordinates with respect to an orthonormal frame field Ei into a sum 1 Rij + 2 Rij + 3 Rij + 4 Rij such that, for any Ei′ = U i i′Ei with...
متن کاملQuaternionic Kähler and Spin(7) Metrics Arising from Quaternionic Contact Einstein Structures
We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic contact manifolds. We prove that the product of the real line with a seven dimensional manifold, equipped with a certain qc structure, has a quaternionic Kähler me...
متن کاملAlmost Kähler 4-manifolds with J-invariant Ricci Tensor and Special Weyl Tensor
for any tangent vectors X,Y to M . If the almost complex structure J is integrable we obtain a Kähler structure. Many efforts have been done in the direction of finding curvature conditions on the metric which insure the integrability of the almost complex structure. A famous conjecture of Goldberg [26] states that a compact almost Kähler, Einstein manifold is in fact Kähler. Important progress...
متن کاملGeometric Structures on Nilpotent Lie Groups: on Their Classification and a Distinguished Compatible Metric
Let (N, γ) be a nilpotent Lie group endowed with an invariant geometric structure (cf. symplectic, complex, hypercomplex or any of their ‘almost’ versions). We define a left invariant Riemannian metric on N compatible with γ to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. We prove that minimal metrics...
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 2003