Results 31 to 40 of about 76,688 (68)
arXiv, 1996 Pluriharmonic maps form an important class of harmonic maps which includes holomorphic maps. We study their morphisms, in particular the inter-relationships between $(1,1)$-geodesic, pluriharmonic and $\pm$holomorphic maps. Then we characterise pluriharmonic morphisms between Hermitian manifolds.
arxiv
The Penrose transform on conformally Bochner-Kähler manifolds [PDF]
arXiv, 1996 We give a generalization of the Penrose transform on Hermitian manifolds with metrics locally conformally equivalent to Bochner-K\"ahler metrics. We also give an explicit formula for the inverse transform. This paper is a generalization of "The Twistor correspondence of the Dolbeault complex over $\C^n$" (dg-ga/9501004) and intended to supersede it.
arxiv
Complex nilmanifolds and K\"ahler-like connections
, 2019 In this note, we analyze the question of when will a complex nilmanifold have K\"ahler-like Strominger (also known as Bismut), Chern, or Riemannian connection, in the sense that the curvature of the connection obeys all the symmetries of that of a K ...
Zhao, Quanting, Zheng, Fangyang
core
Families of (1,2)-Symplectic M etrics on Full Flag Manifolds [PDF]
arXiv, 2000 We obtain new families of (1,2)-symplectic invariant metrics on the full complex flag manifolds F(n). For n > 4, we characterize n-3 different n-dimensional families of (1,2)-symplectic invariant metrics on F(n). Any of these families corresponds to a different class of non-integrable invariant almost complex structure on F(n).
arxiv
Hermitian structures on six dimensional nilmanifolds [PDF]
arXiv, 2004 Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong K\"ahler with torsion, balanced or locally conformal K\"ahler structures (J,g).
arxiv
Homogeneous hypersurfaces in complex hyperbolic spaces [PDF]
arXiv, 2006 We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the homogeneous hypersurfaces together with their multiplicities.
arxiv
Similarity of operators and geometry of eigenvector bundles [PDF]
Publ. Mat. 53 (2009), no. 2, 417--438, 2007 We characterize the contractions that are similar to the backward shift in the Hardy space $H^2$. This characterization is given in terms of the geometry of the eigenvector bundles of the operators.
arxiv
On three-parametric Lie groups as quasi-Kaehler manifolds with Killing Norden metric [PDF]
Topics in Contemporary Differential Geometry, Complex Analysis and
Mathematical Physics, Eds. S. Dimiev and K. Sekigawa, World Sci. Publ.,
Hackensack, NJ, 2007, 205-214, 2008 A 3-parametric family of 6-dimensional quasi-Kaehler manifolds with Norden metric is constructed on a Lie group. This family is characterized geometrically. The condition for such a 6-manifold to be isotropic Kaehler is given.
arxiv
Projective duality and K-energy asymptotics [PDF]
arXiv, 2008 Let X be a smooth, linearly normal n dimensional complex projective variety. Assume that the projective dual of X has codimension one with defining polynomial D(X). In this paper the log of the norm of D(X) is expressed as the restriction to the Bergman metrics of an energy functional on X.
arxiv
Multiplier ideal sheaves and geometric problems [PDF]
arXiv, 2009 In this expository article we first give an overview on multiplier ideal sheaves and geometric problems in K\"ahlerian and Sasakian geometries. Then we review our recent results on the relationship between the support of the subschemes cut out by multiplier ideal sheaves and the invariant whose non-vanishing obstructs the existence of K\"ahler-Einstein
arxiv