INVARIANT f-STRUCTURES IN THE GENERALIZED HERMITIAN GEOMETRY
نویسنده
چکیده
We collect the recent results on invariant f -structures in the generalized Hermitian geometry. Here the canonical f -structures on homogeneous k-symmetric spaces play a remarkable role. Specifically, these structures provide a wealth of invariant examples for the classes of nearly Kähler f -structures, Hermitian f -structures and some others. Finally, we consider all invariant f structures on the complex flag manifold SU(3)/Tmax and describe them in the sense of generalized Hermitian geometry. In particular, it presents first invariant examples of Killing f -structures.
منابع مشابه
INVARIANT METRIC f-STRUCTURES ON SPECIFIC HOMOGENEOUS REDUCTIVE SPACES
For homogeneous reductive spaces G/H with reductive complements decomposable into an orthogonal sum m = m1⊕m2⊕m3 of three Ad(H)invariant irreducible mutually inequivalent submodules we establish simple conditions under which an invariant metric f -structure (f, g) belongs to the classes G1f , NKf , and Kill f of generalized Hermitian geometry. The statements obtained are then illustrated with f...
متن کاملar X iv : m at h / 05 05 66 9 v 1 [ m at h . D G ] 3 1 M ay 2 00 5 INVARIANT RIEMANNIAN METRICS AND f - STRUCTURES ON FLAG MANIFOLDS
It turns out that if a reductive complement m of a homogeneous reductive space G/H possesses a number of properties (including its decomposability into an orthogonal sum of three Ad(H)-invariant irreducible subspaces) then there exists a simple way of determining whether an f -structure F on this space belongs to the classes G1f , NKf and Kill f of generalized Hermitian geometry with respect to...
متن کاملNon-kähler Solvmanifolds with Generalized Kähler Structure
The generalized Kähler structures were introduced and studied by M. Gualtieri in his PhD thesis [16] in the more general context of generalized geometry started by N. Hitchin in [20]. There are many explicit constructions of non-trivial generalized-Kähler structures [1, 2, 21, 24, 25, 4, 7]. For instance Gualtieri proved that all compact-even dimensional semisimple Lie groups are generalized Kä...
متن کاملInvariant f-structures on the flag manifolds SO(n)/SO(2)×SO(n-3)
Invariant structures on homogeneous manifolds are of fundamental importance in differential geometry. Recall that an affinor structure F (i.e., a tensor field F of type (1,1)) on a homogeneous manifold G/H is called invariant (with respect to G) if for any g ∈ G we have dτ(g)◦F = F ◦dτ(g), where τ(g)(xH)= (gx)H . An important place among homogeneous manifolds is occupied by homogeneousΦ-spaces ...
متن کاملHermitian Structures on Cotangent Bundles of Four Dimensional Solvable Lie Groups
We study hermitian structures, with respect to the standard neutral metric on the cotangent bundle T ∗G of a 2n-dimensional Lie group G, which are left invariant with respect to the Lie group structure on T ∗G induced by the coadjoint action. These are in one-to-one correspondence with left invariant generalized complex structures on G. Using this correspondence and results of [8] and [10], it ...
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 2005