6 edition of **Holomorphic vector fields on compact Kähler manifolds.** found in the catalog.

- 352 Want to read
- 31 Currently reading

Published
**1971** by Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society in Providence, R.I .

Written in English

- Geometry, Differential.,
- Manifolds (Mathematics),
- Vector Bundles.

**Edition Notes**

Series | Regional conference series in mathematics,, no. 7 |

Classifications | |
---|---|

LC Classifications | QA1 .R33 no. 7 |

The Physical Object | |

Pagination | vi, 38 p. |

Number of Pages | 38 |

ID Numbers | |

Open Library | OL4577558M |

ISBN 10 | 082181656X |

LC Control Number | 77145641 |

HOLOMORPHIC DISKS AND THREE-MANIFOLD INVARIANTS Then, for each i =0, χ(HF+(Y 0,s 0 +iH)) = ± d j=1 ja |i +j, where s 0 is the Spinc structure with trivial ﬁrst Chern class, and H is a gen- erator for H2(Y 0;Z). Indeed, a variant of Theorem also holds in the case where the ﬁrst. Abstract: This book is an exposition of what is currently known about the fundamental groups of compact Kähler manifolds. This class of groups contains all finite groups and is strictly smaller than the class of all finitely presentable groups. Contents 3 group with values in the sheaf of germs of vector ﬁelds H1(M,£), and are obtained by deriving the transition functions of M with respect to the vari- able ively, an inﬁnitesimal deformation of M may be thought of as a derivative of the complex structure on M, therefore one may wonder whether there exists a process similar to integration to get a family of defor-.

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Holomorphic Vector Fields on Compact Kähler Manifolds Share this page Y. Matsushima. A co-publication of the AMS and CBMS Holomorphic Vector Fields on Compact Kahler Manifolds Base Product Code Compact Kähler Manifolds.

Author(s) (Product display): Y. Matsushima. Publisher Blurb: A co-publication of the AMS and CBMS. Book Series. On any compact complex manifold, the set of all global holomorphic vector fields is a finite dimensional Lie algebra. They span the tangent space at every point just when each component of the manifold is a homogeneous for the action of its biholomorphism group.

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. Highlights We study holomorphic vector fields of compact pseudo-Kähler manifolds. A complex vector field corresponding to a Killing vector field is holomorphic.

There exists a relation between the zero set of a holomorphic vector field and Hodge by: 1. 7. Lichnerowicz, A.: Variétés Kähleriennes et premiere classe de Chern, Journal of Diff. Geom.1, – ().MR 37 # Google ScholarCited by: Kahler manifolds with real holomorphic vector fields. this implies that for a compact K\"{a}hler manifold admitting such a function, there is no nontrivial homomorphism from its first.

Kähler manifolds of semi-negative holomorphic sectional curvature Heier, Gordon, Lu, Steven S. Y., and Wong, Bun, Journal of Differential Geometry, A Uniformization Theorem For Complete Non-compact Kähler Surfaces With Positive Bisectional Curvature Chen, Bing-Long, Tang, Siu-Hung, and Zhu, Xi-Ping, Journal of Differential Geometry, The aim of this book is to give an understandable introduction to the the ory of complex manifolds.

With very few exceptions we give complete proofs. Many examples and figures along with quite a few exercises are included. Our intent is to familiarize the reader with the most important branches and methods in complex analysis of several variables and to do this as simply as possible.

Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Nevertheless, deep results can be proved, for example the Remmert-Stein theorem for analytic sets, finiteness theorems for spaces of cross sections in holomorphic vector bundles, and the solution of the Levi problem.

2 Preliminaries Let (M,g,J) be a 2n-dimensional Hermitian manifold with metric g and complex structure J. The algebra of all C°° vector fields on M will be denoted by XM. The Kahler form Q of the Hermitian structure (g,J) is defined by Q(X,Y) = g(JX,Y); X, Y e XM.

The associated Lee form θ is given by θ = — 50, o J. We denote by V and R = [V, V] — V[] the Levi-Civita connection of the. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share.

compact K¨ahler surfaces [8]. This theory can be easily generalized to arbitrary dimensional compact K¨ahler manifolds, which is a eld theoretical interpretation of intersection parings on the moduli space of stable bundles. In this paper, we propose N = 2 holomorphic Yang-Mills (HYM) theory on compact K¨ahler manifolds.

Our main result is a. part of the general result for the nonexistence of holomorphic sections of a holomorphic vector bundle over a compact Hermitian manifold [21,15] (see also [28,20]). In the present paper we consider questions of existence of harmonic 1-forms, holomorphic.1;0/-forms and ﬁnd relations between them on compact balanced Hermitian manifolds.

holomorphic vector ﬁeld, or as J(∇f) being a Killing vector ﬁeld on M. As we shall see later, the existence of such a function f leads to Liouville type results without involving any curvature conditions.

In the following and throughout the paper, we denote by r(x) the distance function from x to a ﬁxed point p on manifold M. If the volume. We study holomorphic GL(2) and SL(2) geometries on compact complex manifolds. We show that a compact K\"ahler manifold of complex even dimension higher than two admitting a holomorphic GL(2 Author: Daniel Guan.

ON HOLOMORPHIC MAPS INTO COMPACT NON-KÄHLER MANIFOLDS by Masahide KATO & Noboru OKADA Introduction. In this paper, we shall consider the extension problem of holomorphic maps of a Hartogs domain into compact complex manifolds.

Fix an integer n > 2. By a Hartogs domain, we shall mean a domain in complex n-dimensional Euclidean space (Cn defined by. Atiyah{Weil that a holomorphic vector bundle E over M admits a holomorphic connection if and only if each direct summand of Eis of degree zero (see [At2], [We]).

Polystable bundles over a K ahler manifold. A holomorphic vector bundle E over a compact K ahler manifold (M;!) admits a Hermitian{Einstein connection ifand onlyifEispolystable File Size: KB. Theorem A. Let f: X → T be a holomorphic mapping from a compact K¨ahler manifold to a compact complex torus.

Then for j ≥ 0, one has a decomposition Rjf ∗ωX ≃ Mn k=1 q∗ kFk ⊗Lk, where each Fk is an M-regular (hence ample) coherent sheaf with projective support on the compact complex torus Tk, each qk: T → Tk is a surjective File Size: KB.

We prove that a compact lcK manifold with holomorphic Lee vector field is Vaisman provided that either the Lee field has constant norm or the metric is Gauduchon (i.e., the Lee field is divergence-free).

We also give examples of compact lcK manifolds with holomorphic Lee vector field which are not by: 4. Bogomolov, F. Holomorphic tensors and vector bundles on projective manifolds.

Izvestiya Akademii Nauk SSSR Seriya Matematicheskaya, 42(6),Cited by: Center manifolds for holomorphic vector elds in dimension three joint with M. Mcquillan. Singular 1-dimensional foliations F An analytic (real or complex manifold) M An open covering fU ig i2I of M For each i 2I, a vector eld @ i Der O(U i) such that @ i = g ij @ j; on U i \U j for some g ij 2O(U i \U j).

˝ on compact Kähler manifolds [8], and by triples with () such that M is a KÄHLER MANIFOLDS WITH GEODESIC HOLOMORPHIC GRADIENTS 3 KÄHLER MANIFOLDS WITH GEODESIC HOLOMORPHIC GRADIENTS 5 any (y;˘) 2U, cf. Remark. Ricci flow on Kähler-Einstein manifolds Chen, X.

and Tian, G., Duke Mathematical Journal, ; Holomorphic curvatures of almost Kähler manifolds Farran, Hani, Journal of Differential Geometry, ; Three-circle theorem and dimension estimate for holomorphic functions on Kähler manifolds Liu, Gang, Duke Mathematical Journal, Abstract.

We prove that if is a -positive holomorphic line bundle on a compact hyper-kähler manifold, then for with a nonnegative integer. In a special case, and, we recover a vanishing theorem of Verbitsky’s with a little stronger assumption.

Introduction. A hyper-kähler manifold is an oriented -dimensional Riemannian manifold with a special holonomy by: 2.

The theory of manifolds Lecture 4 A vector eld on an open subset, U, of Rn is a function, v, which assigns to each point, p2 U, a vector, v(p) R TpRn. This de nition makes perfectly good sense for manifolds as well.

De nition 1. Let X RN be an n-dimensional manifold. A vector eld on Xis a function, v, which assigns to each point, p2 X, a vector. Holomorphic disks and topological invariants for closed three-manifolds By Peter Ozsvath´ and Zoltan Szab´o* Abstract The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y, equipped with a Spinc structure.

Given a Heegaard splitting of Y = U 0 ∪ Σ U 1, these theories are variants of the. for vector fields w on compact Riemannian manifolds (M, g), obvious from (), the conclusion that in any compact Kähler manifold (M, g) the operator D is nonnegative and its kernel consists precisely of all of holomorphic vector fields: () Ker D = h(M), obtained as a direct consequence of the relation.

Vector fields in n-dimension manifolds 3 that each 1 T p [0 ≤ p ≤ k] of 1 Tk corresponds to a 2 T p of 2 Tk, while two points A 1, A2 of 1 Tn, 2 Tn that do not belong to 1 Tk, 2 Tk are not associated with each other. This association is transitive − i.e.: if, on the one hand, A1, File Size: KB.

Introduction to Extremal metrics Preliminary version G abor Sz ekelyhidi Contents 1 K ahler geometry2 Holomorphic vector elds and the Futaki invariant File Size: KB. [Lu] Y.C. Lu, Holomorphic mappings of complex manifolds, J.

Diff. Geom.2 (), Zbl MR [Y] S.T. Yau, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana by: Let M be an n-dimensional K¨ahler manifold, L.

M be a ﬂat line bundle, SV. M be a ﬂat holomorphic symplectic vector bundle of rank 2n, and consider the tensor bundle H = SV ›L. Deﬁnition A K¨ahler manifold M is rigid special K¨ahler, if there is a section Ω 2 Γ(H;M) such that the K¨ahler form is given by J = i 2 @@¯hΩjΩi together with the condition [email protected]Ω[email protected]Ωi = 0File Size: KB.

In differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup of Sp(n)Sp(1) for some ≥.Here Sp(n) is the sub-group of () consisting of those orthogonal transformations that arise by left-multiplication by some quaternionic × matrix, while the group () ≈ of unit-length quaternions.

on compact complex manifolds and holomorphic deformations. In this talk we focus on the interaction of several complex invariants and metric properties of compact complex manifolds, as well as their behaviour under holomorphic deformations. Strongly Gauduchon (sG) metrics were introduced by.

the ball. Until now there is no known example of a compact Kaihler mani-fold of negative sectional curvature which does not admit a Kghler metric with strongly negative curvature tensor. Our result is proved by showing that a harmonic map of compact Kiihler manifolds is either holomorphic or conjugate holomorphic if the rank over.

what are the holomorphic functions. Any holomorphic function gives a bounded entire function by removing a point, and so must be constant. This is in fact true for holomorphic functions on compact connected complex manifolds.

Theorem The only global holomorphic functions on a compact connected complex manifold are the constants. Corollary Complex Manifolds Lecture notes based on the course by Lambertus van Geemen A.A. / Author: Michele Ferrari. A holomorphic atlas (or complex analytical atlas) of X is a collection A= f(U ;z)goflocalcomplexcharts,suchthatX= We notice that Pn is compact: let S2n+1 = fu2Cn+1 jjjujj= pP juFile Size: KB.

Extremal metrics and stabilities on polarized manifolds m-th Bergman kernel Bm,ω for the Kähler manifold (M,ω) is characterized as the Fourier coefﬁcient pr∗ Bm,ω:= n. mn S1 e−imθS ω(e iθx,x)dθ. Now the Bergman kernel is deﬁned not only for positive integers m but also for complexnumbersξ asfollows.

Toseethesituation,weﬁrstconsiderthecasewhereM is a single point. Our work is concerned with the relation between a complex differential geometric property, namely holomorphicity, and a metric one, namely to be conformal and minimal, of immersions (possibly branched) of Riemann surfaces into Kahler manifolds.

A well known theorem (Wirtinger's Inequality) states that every holomorphic surface inside a Kahler manifold is area minimizing w.r.t. variations with. HOLOMORPHIC DYNAMICS ON PROJECTIVE SURFACES 4 Aims and scope.

This text describes the dynamics of automorphisms of compact complex surfaces when it is rich, as in the example f = s1 s2 s3 above. We restrict the study to compact Kähler surfaces.

This is justiﬁed by the fact that the topological entropy of all automorphisms vanishes on. on which η = df with f holomorphic and x,y are in U and are in the same connected component of a ﬁber of f. Theorem ([DG05, ]). — Let X be a complete Kahler manifold of bounded geometry, η a closed holomorphic 1-form on X and Fη the associated singular holomorphic foliation.

If Fη has one compact leaf, all leaves are compact. holomorphic sections of powers LN of a positive holomorphic line bundle L on a compact Kähler manifold M.

The Bergman kernel KN(z,w) for LN → M is the kernel of the orthogonal projection from the space of L2 sections of LN to the holo-morphic sections. InTian [27] gave the leading asymptotics of the diagonal Communicated by Marco M.A. G. Sergeev, “Kähler Geometry of the Universal Teichmüller Space and Coadjoint Orbits of the Virasoro Group”, Proc.

Steklov Inst. Math., (), – A. G. Sergeev, “Harmonic maps into loop spaces of compact Lie groups”, Supersymmetries and quantum symmetries, Joint Inst.

for Nuclear Res., Dubna,– vanishing theorem for a compact irreducible hyper-k ¨ahler manifold. eorem (Verbitsky, [ ]). Let be a compact irre-ducible hyper-k ahler manifold of real dimension¨ 4,andlet be a holomorphic line bundle 0 = 1 () K,in particular, if is a positive line bundle, then (,) =0, for >.

Verbitsky s proof of the above theorem is a clever useCited by: 2.