On the sum of the Hermitian scalar curvatures of a compact Hermitian manifold

1987 ◽  
Vol 195 (3) ◽  
pp. 429-432 ◽  
Author(s):  
Andrew Balas
Keyword(s):  
Hermitian Manifold ◽  
Compact Hermitian Manifold

scholarly journals Hermitian Harmonic Maps into Convex Balls

2007 ◽  
Vol 50 (1) ◽  
pp. 113-122 ◽  
Author(s):  
Zhen Yang Li ◽  
Xi Zhang
Keyword(s):  
Dirichlet Problem ◽  
Heat Flow ◽  
Harmonic Maps ◽  
Hermitian Manifold ◽  
Flow Method ◽  
Hermitian Manifolds ◽  
Compact Hermitian Manifold

AbstractIn this paper, we consider Hermitian harmonic maps from Hermitian manifolds into convex balls. We prove that there exist no non-trivial Hermitian harmonic maps from closed Hermitian manifolds into convex balls, and we use the heat flow method to solve the Dirichlet problem for Hermitian harmonic maps when the domain is a compact Hermitian manifold with non-empty boundary.

ON THE GROWTH OF HOLOMORPHIC PROJECTIVE FOLIATIONS

2002 ◽  
Vol 13 (07) ◽  
pp. 695-726 ◽  
Author(s):  
B. C. AZEVEDO SCÁRDUA ◽  
J. C. CANILLE MARTINS
Keyword(s):  
Algebraic Curves ◽  
Hermitian Manifold ◽  
Holomorphic Foliation ◽  
Global Dynamics ◽  
Subexponential Growth ◽  
Codimension One ◽  
Singular Foliations ◽  
Invariant Algebraic Curves ◽  
Dimension One ◽  
Compact Hermitian Manifold

In the theory of real (non-singular) foliations, the study of the growth of the leaves has proved to be useful in the comprehension of the global dynamics as the existence of compact leaves and exceptional minimal sets. In this paper we are interested in the complex version of some of these basic results. A natural question is the following: What can be said of a codimension one (possibly singular) holomorphic foliation on a compact hermitian manifold M exhibiting subexponential growth for the leaves? One of the first examples comes when we consider the Fubini–Study metric on [Formula: see text] and dimension one foliations. In this case, under some non-degeneracy hypothesis on the singularities, we may classify the foliation as a linear logarithmic foliation. In particular, the limit set of ℱ is a union of singularities and invariant algebraic curves. Applications of this and other results we prove are given to the general problem of uniformization of the leaves of projective foliations.

scholarly journals Continuous solutions to Monge–Ampère equations on Hermitian manifolds for measures dominated by capacity

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Sławomir Kołodziej ◽  
Ngoc Cuong Nguyen
Keyword(s):  
Hermitian Manifold ◽  
General Measure ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Hermitian Manifolds ◽  
Right Hand ◽  
The Right ◽  
Monge Ampere ◽  
Compact Hermitian Manifold

AbstractWe prove the existence of a continuous quasi-plurisubharmonic solution to the Monge–Ampère equation on a compact Hermitian manifold for a very general measure on the right hand side. We admit measures dominated by capacity in a certain manner, in particular, moderate measures studied by Dinh–Nguyen–Sibony. As a consequence, we give a characterization of measures admitting Hölder continuous quasi-plurisubharmonic potential, inspired by the work of Dinh–Nguyen.

scholarly journals GEOMETRY OF HERMITIAN MANIFOLDS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250055 ◽  
Author(s):  
KE-FENG LIU ◽  
XIAO-KUI YANG
Keyword(s):  
Vector Bundle ◽  
Ricci Curvature ◽  
Vector Bundles ◽  
Hermitian Manifold ◽  
Geometric Flow ◽  
Complex Vector ◽  
Hermitian Manifolds ◽  
Metric Connection ◽  
Curvature Tensors ◽  
Compact Hermitian Manifold

On Hermitian manifolds, the second Ricci curvature tensors of various metric connections are closely related to the geometry of Hermitian manifolds. By refining the Bochner formulas for any Hermitian complex vector bundle (and Riemannian real vector bundle) with an arbitrary metric connection over a compact Hermitian manifold, we can derive various vanishing theorems for Hermitian manifolds and complex vector bundles by the second Ricci curvature tensors. We will also introduce a natural geometric flow on Hermitian manifolds by using the second Ricci curvature tensor.

Conformal transformation in an almost Hermitian manifold

2016 ◽  
Vol 46 (1) ◽  
pp. 217-226
Author(s):  
B. B. Chaturvedi ◽  
Pankaj Pandey
Keyword(s):  
Conformal Transformation ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold

On submersions of the complex indicatrix

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5081-5092
Author(s):  
Elena Popovicia
Keyword(s):  
Fixed Point ◽  
Complex Projective Space ◽  
Finsler Space ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Codimension One ◽  
Real Submanifold ◽  
Fundamental Equations ◽  
Complex Projective ◽  
Extrinsic Sphere

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

scholarly journals Moduli Space of Brody Curves, Energy and Mean Dimension

2008 ◽  
Vol 192 ◽  
pp. 27-58 ◽  
Author(s):  
Masaki Tsukamoto
Keyword(s):  
Complex Plane ◽  
Moduli Space ◽  
Hermitian Manifold ◽  
Value Distribution ◽  
Holomorphic Map ◽  
Infinite Dimensional ◽  
Mean Dimension ◽  
The Mean ◽  
Moduli Theory ◽  
Bounded Derivative

AbstractA Brody curve is a holomorphic map from the complex plane ℂ to a Hermitian manifold with bounded derivative. In this paper we study the value distribution of Brody curves from the viewpoint of moduli theory. The moduli space of Brody curves becomes infinite dimensional in general, and we study its “mean dimension”. We introduce the notion of “mean energy” and show that this can be used to estimate the mean dimension.

The Heat Equation for the -Neumann Problem, II

1988 ◽  
Vol 40 (2) ◽  
pp. 502-512 ◽  
Author(s):  
Richard Beals ◽  
Nancy K. Stanton
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Neumann Problem ◽  
Elliptic Boundary ◽  
Neumann Boundary ◽  
Hermitian Manifold ◽  
Neumann Boundary Conditions ◽  
Compact Manifolds ◽  
Elliptic Boundary Value ◽  
Image Position

Let Ω be a compact complex n + 1-dimensional Hermitian manifold with smooth boundary M. In [2] we proved the following.THEOREM 1. Suppose satisfies condition Z(q) with 0 ≦ q ≦ n. Let □p,q denote the -Laplacian on (p, q) forms onwhich satisfy the -Neumann boundary conditions. Then as t → 0;,(0.1)(If q = n + 1, the -Neumann boundary condition is the Dirichlet boundary condition and the corresponding result is classical.)Theorem 1 is a version for the -Neumann problem of results initiated by Minakshisundaram and Pleijel [8] for the Laplacian on compact manifolds and extended by McKean and Singer [7] to the Laplacian with Dirichlet or Neumann boundary conditions and by Greiner [5] and Seeley [9] to elliptic boundary value problems on compact manifolds with boundary. McKean and Singer go on to show that the coefficients in the trace expansion are integrals of local geometric invariants.

On 4-dimensional generalized complex space forms

1999 ◽  
Vol 66 (3) ◽  
pp. 379-387 ◽  
Author(s):  
Un Kyu Kim
Keyword(s):  
Sectional Curvature ◽  
Complex Space ◽  
Hermitian Manifold ◽  
Holomorphic Sectional Curvature ◽  
Space Forms ◽  
Generalized Complex ◽  
Complex Forms ◽  
Complex Space Forms

AbstractWe characterize four-dimensional generalized complex forms and construct an Einstein and weakly *-Einstein Hermitian manifold with pointwise constant holomorphic sectional curvature which is not globally constant.

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