Published in Frontiers of Mathematics in China
Let Dn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathscr{D}_n$$\end{document} be the multicomponent twisted Heisenberg-Virasoro algebra. We compute the second con...
Published in Science China Mathematics
Let H be a Hilbert space and A ⊆ B(H) a C*-subalgebra. This paper is devoted to studying the set GP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curves. We prove that the space GP is a C∞ Banach submanifold of A, and a homogeneous reductive space under the action of Banach Lie group UA ...
Published in Mathematical Physics, Analysis and Geometry
Let G be a Lie group of even dimension and let (g, J) be a left invariant anti-Kähler structure on G. In this article we study anti-Kähler structures considering the distinguished cases where the complex structure J is abelian or bi-invariant. We find that if G admits a left invariant anti-Kähler structure (g, J) where J is abelian then the Lie alg...
Published in Acta Mathematica Sinica, English Series
Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieti...
Published in Mathematische Annalen
We generalize the notion of the density property for complex manifolds to holomorphic fibrations, and introduce the notion of the fibred density property. We prove that the natural fibration of the spectral ball over the symmetrized polydisc enjoys the fibred density property and describe the automorphism group of the spectral ball.
Published in Annals of Global Analysis and Geometry
Let X be a connected complex manifold equipped with a holomorphic action of a complex Lie group G. We investigate conditions under which a principal bundle on X admits a G-equivariance structure.
Published in Annals of Global Analysis and Geometry
We describe the generalized Kuranishi spaces of solvmanifolds with left-invariant complex structures. By using such description, we study the stability of left-invariantness of deformed generalized complex structures and smoothness of generalized Kuranishi spaces on certain classes of solvmanifolds. We also give explicit finite-dimensional cochain ...
Published in The Journal of Geometric Analysis
In our joint article with N. Kruzhilin of 2002, we showed that every connected complex manifold of dimension n≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 2$$...
Published in The Journal of Geometric Analysis
We obtain an explicit formula of the Bergman kernel for Hartogs domains over bounded homogeneous domains. In order to find a simple formula, we consider a Siegel domain biholomorphic to the bounded homogeneous domain and use its Bergman kernel obtained by Gindikin. The Bergman kernel of the Hartogs domain is expressed by two different forms and the...
Published in Ricerche di Matematica
Let G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G$$\end{document} be a quasi-Hermitian Lie group and let K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepa...
