Wu, Yemo Xu, Xiurong Zuo, Dafeng
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...

Cui, Miaomiao Ji, Guoxing
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 ...

Fernández-Culma, Edison Alberto Godoy, Yamile
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...

Kim, Shin-Young Park, Kyeong-Dong
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...

Andrist, Rafael B. Kutzschebauch, Frank
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.

Biswas, Indranil Paul, Arjun
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.

Kasuya, Hisashi
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 ...

Isaev, Alexander
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}$$n\ge 2$$...

Ishi, Hideyuki Park, Jong-Do Yamamori, Atsushi
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...

Cahen, Benjamin
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...