一类全纯映射的增长性

§ 1.　NotationsandFormulas　　Let(N ,dS2 N)beaHermitianmanifoldofdimensionn ,anddS2 NitsHermitianmertric.Let{e1～ ,Λen～}oftype (1 ,0 )tangentvectorsconstitutealocalunitaryframefieldinanopensetofM .Let{ω1 ,Λωn}betheunitarycoframewhichconsistsofncomplex valuedlineardifferen tialformsoftype (1 ,0 )suchthatdS2 N =ωαω-α. (1 )Hereandbelowthesummationconventionisused ,i.e .,therepeatedindexmeanssummation .LetBbethebundleofallunitaryframesofN .Thentheforms{ωα}areformsinB .Itiswellkn…     

Semistable Twisted Holomorphic Chains on Non-Compact Kähler Manifolds

In this paper, the author proves a generalized Donaldson-Uhlenbeck-Yau theorem for twisted holomorphic chain on a non-compact K\"ahler manifold. As an application, the author obtains a Bogomolov type Chern numbers inequality for semistable twisted holomorphic chain.     

Stable bundles, representation theory and Hermitian operators

We give an interpretation and a solution of the classical problem of the spectrum of the sum of Hermitian matrices in terms of stable bundles on the projective plane.     

UNIFORM ESTIMATES OF SOLUTIONS OF (δ)-EQUATION ON STEIN MANIFOLDS

By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for (p, q) differential forms on an open set with C1 piecewise smooth boundary on a Stein manifold, and under suitable conditions gave the solutions of (δ)-equation on a Stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of (δ)-equation for (p, q) differential forms on a Stein manifold.     

Geometric properties of almost contact metric 3-submersions

Summary In this paper, we discuss some geometric properties of three types of Riemannian submersions whose total space is an almost contact metric manifold with 3-structure. The study is focused on the transference of structures.     

UNIFORM ESTIMATES OF SOLUTIONS OF δ^--EQUATION ON STEIN MANIFOLDS

By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for （p, q） differential forms on an open set with C^1 piecewise smooth boundary on a Stein manifold, and under suitable conditions gave the solutions of δ^--equation on a Stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of δ^--equation for （p, q） differential forms on a Stein manifold.     

On the Bergman representative coordinates

We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the Bergman metric contained in this set. By concrete examples we show that these estimates are the best possible.     

On the intersection of Hermitian curves and of Hermitian surfaces

Kestenband [Unital intersections in finite projective planes, Geom. Dedicata 11(1) (1981) 107–117; Degenerate unital intersections in finite projective planes, Geom. Dedicata 13(1) (1982) 101–106] determines the structure of the intersection of two Hermitian curves of PG(2,q²), degenerate or not. In this paper we give a new proof of Kestenband's results. Giuzzi [Hermitian varieties over finite field, Ph.D. Thesis, University of Sussex, 2001] determines the structure of the intersection of two non-degenerate Hermitian surfaces and of PG(3,q²) when the Hermitian pencil defined by and contains at least one degenerate Hermitian surface. We give a new proof of Giuzzi's results and we obtain some new results in the open case when all the Hermitian surfaces of the Hermitian pencil are non-degenerate.     

Derivation techniques on the Hermitian surface

We discuss derivation‐like techniques for transforming one locally Hermitian partial ovoid of the Hermitian surface H(3,q²) into another one. These techniques correspond to replacing a regulus by its opposite in some naturally associated projective 3‐space PG(3,q) over a square root subfield. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 478–486, 2007     

The geometry of L-manifolds

A class of almost contact metric structures generalizing those of quasi-Sasakian and trans-Sasakian structures is introduced and studied. Its subclass consisting of normal structures locally conformal to quasi-Sasakian structures is investigated in detail.     

Heat Flow for the Yang–Mills–Higgs Field and the Hermitian Yang–Mills–Higgs Metric

For a parameter > 0, we study a type of vortex equations, which generalize the well-known Hermitian–Einstein equation, for a connection A and a section of a holomorphic vector bundle E over a Kähler manifold X. We establish a global existence of smooth solutions to heat flow for a self-dual Yang–Mills–Higgs field on E. Assuming the -stability of (E, ), we prove the existence of the Hermitian Yang–Mills–Higgs metric on the holomorphic bundle E by studying the limiting behaviour of the gauge flow.     

Intrinsic Data Depth for Hermitian Positive Definite Matrices

Nondegenerate covariance, correlation, and spectral density matrices are necessarily symmetric or Hermitian and positive definite. This article develops statistical data depths for collections of Hermitian positive definite matrices by exploiting the geometric structure of the space as a Riemannian manifold. The depth functions allow one to naturally characterize most central or outlying matrices, but also provide a practical framework for inference in the context of samples of positive definite matrices. First, the desired properties of an intrinsic data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two pointwise and integrated data depth functions that satisfy each of these requirements and investigate several robustness and efficiency aspects. As an application, we construct depth-based confidence regions for the intrinsic mean of a sample of positive definite matrices, which is applied to the exploratory analysis of a collection of covariance matrices in a multicenter clinical trial. Supplementary materials and an accompanying R-package are available online.     

Compact Hermitian surfaces of constant antiholomorphic sectional curvatures

Compact Hermitian surfaces of constant antiholomorphic sectional curvatures with respect to the Riemannian curvature tensor and with respect to the Hermitian curvature tensor are considered. It is proved: a compact Hermitian surface of constant antiholomorphic Riemannian sectional curvatures is a self-dual Kaehler surface; a compact Hermitian surface of constant antiholomorphic Hermitian sectional curvatures is either a Kaehler surface of constant (non-zero) holomorphic sectional curvatures or a conformally flat Hermitian surface.