arXiv research

The paper explores Kähler-like metrics on generalized flag manifolds.

The paper classifies flag manifolds with specific isotropy components and finds conditions for Kähler-like scalar curvature.

Researchers classify invariant Hermitian structures on flag manifolds with parallel Bismut torsion.

The paper examines the geometry of specific submanifolds in flag manifolds.

The paper classifies structures on complex flag manifolds and provides examples.

The paper describes Hermitian non-Kähler structures on complex flag manifolds.

Geometric bijection and homotopy equivalence between Lie group orbits.

Study of zonal spherical functions on partial flag manifolds using Jacobi polynomials.

Study shows only one type of proper domain in certain spaces.

Abstract: Study cohomology of flag bundles over compact Hermitian locally symmetric spaces.

We study the index of symmetry of a compact generalized flag manifold M=G/H endowed with an invariant Kaehler structure. When the group G is simple we show that the leaves of symmetry are irreducible Hermitian symmetric spaces and we estimate their dimension.

The study characterizes real flag manifolds with invariant generalized almost complex structures.

The study characterizes compact homogeneous manifolds with Bismut parallel torsion.

A hermitian algebra is a unital associative ${\mathbb C}$-algebra endowed with an involution such that the spectra of self-adjoint elements are contained in ${\mathbb R}$. In the case of an algebra ${\mathcal A}$ endowed with a Mackey-complete, locally convex topology such that the set of invertible elements is open an…

Quantum flag manifold σ-models are integrable and satisfy Ricci flow equations.

For a Kähler Manifold $M$, the "symplectic Dolbeault operators" are defined using the symplectic spinors and associated Dirac operators, in complete analogy to how the usual Dolbeault operators, $\bar\partial$ and $\bar\partial^*$, arise from Dirac operators on the canonical complex spinors on $M$. We give special atte…

We consider manifolds of oriented flags SO(n)/SO(2)xSO(n-3) (n>=4) as 4- and 6-symmetric spaces and indicate characteristic conditions for invariant Riemannian metrics under which the canonical f-structures on these homogeneous $Φ$-spaces belong to the classes Kill f, NKf and G_1f of generalized Hermitian geometry.

Classifies G1 structures on flag manifolds using t-roots.

This paper constructs Brownian motion on complex flag manifolds and finds joint distribution of stochastic areas.

New examples of deformed Hermitian-Yang-Mills connections found.

Let $G$ be a complex simple direct limit group, specifically $SL(\infty;\mathbb{C})$, $SO(\infty;\mathbb{C})$ or $Sp(\infty;\mathbb{C})$. Let $\mathcal{F}$ be a (generalized) flag in $\mathbb{C}^\infty$. If $G$ is $SO(\infty;\mathbb{C})$ or $Sp(\infty;\mathbb{C})$ we suppose further that $\mathcal{F}$ is isotropic. Let…

The study finds Lagrangian submanifolds in adjoint semisimple orbits for real forms.

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 Kaehler f-structures, Hermitian f-struc…

Researchers find spectral gaps in quantum flag manifolds using twisted operators.

The paper classifies special Randers metrics on Lie groups.

For homogeneous reductive spaces G/H with reductive complements decomposable into an orthogonal sum \mathfrak{m}=\mathfrak{m}_1 \oplus \mathfrak{m}_2 \oplus \mathfrak{m}_3 of three Ad(H)-invariant irreducible mutually inequivalent submodules we establish simple conditions under which an invariant metric f-structure (f,…

Study subgroups preserving proper domains in flag manifolds.

A Hermitian metric $ω$ on a complex manifold is called SKT or pluriclosed if $dd^cω=0$. Let M be a twistor space of a compact, anti-selfdual Riemannian manifold, admitting a pluriclosed Hermitian metric. We prove that in this case M is Kähler, hence isomorphic to $\C P^3$ or a flag space. This result is obtained from r…

The moduli space NK of infinitesimal deformations of a nearly Kähler structure on a compact 6-dimensional manifold is described by a certain eigenspace of the Laplace operator acting on co-closed primitive (1,1) forms. Using the Hermitian Laplace operator and some representation theory, we compute the space NK on all 6…

The article finds non-Abelian DT-instantons on non-Kähler manifolds.

We calculate the Chern classes and Chern numbers for the natural almost Hermitian structures of the partial flag manifolds F_n=SU(n+2)/S(U(n)\times U(1)\times U(1)). For all n>1 there are two invariant complex algebraic structures, which arise from the projectivizations of the holomorphic tangent and cotangent bundles …

The so-called Hitchin-Kobayashi correspondence, proved by Donaldson, Uhlenbeck and Yau, establishes that an indecomposable holomorphic vector bundle over a compact Kahler manifold admits a Hermitian-Einstein metric if and only if the bundle satisfies the Mumford-Takemoto stability condition. In this paper we consider a…

Study open orbits in causal flag manifolds with applications in AQFT.

Let $G$ be a simple compact connected Lie group. We study homogeneous Einstein metrics for a class of compact homogeneous spaces, namely generalized flag manifolds $G/H$ with second Betti number $b_{2}(G/H)=1$. There are 8 infinite families $G/H$ corresponding to a classical simple Lie group $G$ and 25 exceptional flag…

In the present paper we study Randers metics of Berwald type on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. On these spaces, the Randers metrics arising from invariant hyper-Hermitian metrics are considered. Then we give explicit formulas for computing flag curvature of th…

We classify six-dimensional homogeneous nearly Kähler manifolds and give a positive answer to Gray and Wolf's conjecture: every homogeneous nearly Kähler manifold is a Riemannian 3-symmetric space equipped with its canonical almost Hermitian structure. The only four examples in dimension 6 are $S^3 \times S^3$, the com…

Study of $t$-Gauduchon Ricci-flat condition under Chern-Ricci flow on non-Kähler manifolds.

Condition for intersection of real flag manifolds in complex flag manifold.

Proves a formula for push-forward of polynomial Chern forms in universal vector bundles.

We introduce the notion of $T$-stability for torsion-free Higgs sheaves as a natural generalization of the notion of $T$-stability for torsion-free coherent sheaves over compact complex manifolds. We prove similar properties to the classical ones for Higgs sheaves. In particular, we show that only saturated flags of to…

Study non-split supermanifolds from complex manifolds.

New algorithm computes flag mean and median on flag manifolds.

Minimal dimensions found for flag manifolds embeddings.

Study equigeodesics on $G_2$-type flag manifolds, splitting tangent spaces.

Study finds conditions for Kähler-Einstein metrics on flag manifolds.

Study of weighted nonlinear flags in symplectic geometry.

The paper studies Finsler manifolds with a new curvature concept.

Conditions found for flag manifolds to use Bochner coordinates.