共查询到20条相似文献,搜索用时 35 毫秒
1.
Sorin Dumitrescu 《Comptes Rendus Mathematique》2009,347(19-20):1183-1187
We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine connections. To cite this article: S. Dumitrescu, C. R. Acad. Sci. Paris, Ser. I 347 (2009). 相似文献
2.
Sorin Dumitrescu 《Monatshefte für Mathematik》2010,19(2):145-154
We study local automorphisms of holomorphic Cartan geometries. This leads to classification results for compact complex manifolds admitting holomorphic Cartan geometries. We prove that a compact Kähler Calabi–Yau manifold bearing a holomorphic Cartan geometry of algebraic type admits a finite unramified cover which is a complex torus. 相似文献
3.
Zbigniew Olszak 《Central European Journal of Mathematics》2009,7(3):442-451
For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct examples of non-compact essentially holomorphically pseudosymmetric Kählerian manifolds. These examples show that the compactness assumption cannot be omitted in the above stated theorem. Recently, the first examples of compact, simply connected essentially holomorphically pseudosymmetric Kählerian manifolds are discovered in [4]. In these examples, the structure functions change their signs on the manifold. 相似文献
4.
Xu Cheng 《Geometriae Dedicata》2002,90(1):115-125
In this paper, we consider the coisotropic submanifolds in a Kähler manifold of nonnegative holomorphic curvature. We prove an intersection theorem for compact totally geodesic coisotropic submanifolds and discuss some topological obstructions for the existence of such submanifolds. Our results apply to Lagrangian submanifolds and real hypersurfaces since the class of coisotropic submanifolds includes them. As an application, we give a fixed-point theorem for compact Kähler manifolds with positive holomorphic curvature. Also, our results can be further extended to nearly Kähler manifolds. 相似文献
5.
Martin Svensson 《manuscripta mathematica》2002,107(1):1-13
We study holomorphic harmonic morphisms from K?hler manifolds to almost Hermitian manifolds. When the codomain is also K?hler
we get restrictions on such maps in the case of constant holomorphic curvature. We also prove a Bochner-type formula for holomorphic
harmonic morphisms which, under certain curvature conditions of the domain, gives insight to the structure of the vertical
distribution. We thus prove that when the domain is compact and non-negatively curved, the vertical distribution is totally
geodesic.
Received: 28 May 2001 相似文献
6.
We investigate relative holomorphic connections on a principal bundle over a family of compact complex manifolds. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic principal bundle over a complex analytic family. We also introduce the notion of relative equivariant bundles and establish its relation with relative holomorphic connections on principal bundles. 相似文献
7.
In this note we show that on any compact subdomain of a Kähler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to the linearized anisotropic Calderón problem on a class of complex manifolds that includes compact subdomains of Stein manifolds and sufficiently small subdomains of Kähler manifolds. Some of these manifolds do not admit limiting Carleman weights, and thus cannot be treated by standard methods for the Calderón problem in higher dimensions. The argument is based on constructing Morse holomorphic functions with approximately prescribed critical points. This extends earlier results from the case of Riemann surfaces to higher dimensional complex manifolds. 相似文献
8.
Laurent Meersseman 《Mathematische Annalen》2000,317(1):79-115
We consider holomorphic linear foliations of dimension m of (with ) fulfilling a so-called weak hyperbolicity condition and equip the projectivization of the leaf space (for the foliation
restricted to an adequate open dense subset) with a structure of compact, complex manifold of dimension . We show that, except for the limit-case where we obtain any complex torus of any dimension, this construction gives non-symplectic manifolds, including the previous
examples of Hopf, Calabi-Eckmann, Haefliger (linear case), Loeb-Nicolau (linear case) and López de Medrano-Verjovsky. We study
some properties of these manifolds, that is to say meromorphic functions, holomorphic vector fields, forms and submanifolds.
For each manifold, we construct an analytic space of deformations of dimension and show that, under some additional conditions, it is universal. Lastly, we give explicit examples of new compact, complex
manifolds, in particular of connected sums of products of spheres and show the existence of a momentum-like map which classifies
these manifolds, up to diffeomorphism.
Received: 28 October 1998 / in final form: 7 September 1999 相似文献
9.
Laura Scull 《Mathematische Zeitschrift》2007,257(3):547-562
We consider simply connected compact Kähler manifolds which have a holomorphic action of a torus group. We use the existing equivariant models for rational homotopy to show that these spaces satisfy an equivariant formality condition over the complex numbers. 相似文献
10.
Nobuhiro Honda 《Mathematische Annalen》2001,319(3):469-481
Meromorphicity is the most basic property for holomorphic -actions on compact complex manifolds. We prove that the meromorphicity of -actions on compact complex manifolds are not necessarily preserved by small deformations, if the complex dimension of complex
manifolds is greater than two. In contrast, we also show that the meromorphicity of -actions on compact complex surface depends only on the topology (the first Betti number) of the surface. We construct such
examples of dimension greater than two by studying an equivariant deformation of certain complex threefold, so called a twistor
space.
Received January 25, 2000 / Published online October 30, 2000 相似文献
11.
We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these objects. As consequence, we give some applications to holomorphic foliations tangent to real-analytic Levi-flat hypersurfaces with singularities in \(\mathbb {P}^2\). 相似文献
12.
We use the Borel-Weil scheme for the construction of irreducible representations of compact Lie groups in the spaces of holomorphic
sections of line bundles over homogeneous manifolds. We find the explicit form of the space of sections and construct an invariant
scalar product. We show that the space of holomorphic sections locally satisfies the Zhelobenko indicator system.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 10, pp. 1316–1323, October, 1998. 相似文献
13.
Włodzimierz Jelonek 《Annals of Global Analysis and Geometry》2009,36(2):143-159
The aim of this article is to classify compact Kähler manifolds with quasi-constant holomorphic sectional curvature. 相似文献
14.
S. M. Ivashkovitch 《Journal of Geometric Analysis》1992,2(4):351-371
In this paper we study the extension properties of holomorphic and meromorphic maps into complex manifolds that carry a pluriclosed Hermitian metric. For example, any compact, complex surface admits such a metric. We prove that the only obstructions for the Hartogs-type extendability of holomorphic maps are spherical shells and rational curves. 相似文献
15.
Finnur Lárusson 《Mathematische Zeitschrift》2012,272(3-4):1051-1058
We investigate the behaviour of the Oka property with respect to deformations of compact complex manifolds. We show that in a family of compact complex manifolds, the set of Oka fibres corresponds to a G δ subset of the base. We give a necessary and sufficient condition for the limit fibre of a sequence of Oka fibres to be Oka in terms of a new uniform Oka property. We show that if the fibres are tori, then the projection is an Oka map. Finally, we consider holomorphic submersions with noncompact fibres. 相似文献
16.
We study holomorphic automorphisms on compact Kähler manifolds having simple actions on the Hodge cohomology ring. We show for such automorphisms that the main dynamical Green currents admit complex laminar structures (woven currents) and the Green measure is the unique invariant probability measure of maximal entropy. 相似文献
17.
N. Blažić M. Prvanović 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2001,71(1):35-47
Let(M, g, J) be an almost Hermitian manifold. In this paper we study holomorphically nonnegatively(δ,Δ)-pinched almost Hermitian manifolds. In [3] it was shown that for such Kahler manifolds a plane with maximal sectional curvature
has to be a holomorphic plane(J-invariant). Here we generalize this result to arbitrary almost Hermitian manifolds with respect to the holomorphic curvature
tensorH R and toRK-manifolds of a constant type λ(p). In the proof some estimates of the sectional curvature are established. The results obtained are used to characterize almost
Hermitian manifolds of constant holomorphic sectional curvature (with respect to holomorphic and Riemannian curvature tensor)
in terms of the eigenvalues of the Jacobi-type operators, i.e. to establish partial cases of the Osserman conjecture. Some
examples are studied.
The first author is partially supported by SFS, Project #04M03. 相似文献
18.
Andrew M. Zimmer 《Geometriae Dedicata》2017,190(1):81-102
In this paper we study the set of projective maps between compact properly convex real projective manifolds. We show that this set contains only finitely many distinct homotopy classes and each homotopy class has the structure of a real projective manifold. When domain is irreducible and the target is strictly convex, our results imply that each non-trivial homotopy class contains at most one projective map. These results are motivated by the theory of holomorphic maps between compact complex manifolds. 相似文献
19.
Paul-Andi Nagy 《Journal of Geometric Analysis》2003,13(4):659-667
We study Riemannian foliations with complex leaves on Kähler manifolds. The tensor T, the obstruction to the foliation be totally geodesic, is interpreted as a holomorphic section of a certain vector bundle. This enables us to give classification results when the manifold is compact. 相似文献
20.
V. K. Beloshapka V. V. Ezhov G. Schmalz 《Proceedings of the Steklov Institute of Mathematics》2006,253(1):1-7
We study real analytic CR manifolds of CR dimension 1 and codimension 2 in the three-dimensional complex space. We prove that the germ of a holomorphic mapping between “nonspherical” manifolds can be extended along any path (this is an analog of Vitushkin’s germ theorem). For a cubic model surface (“sphere”), we prove an analog of the Poincaré theorem on the mappings of spheres into ?2. We construct an example of a compact “spherical” submanifold in a compact complex 3-space such that the germ of a mapping of the “sphere” into this submanifold cannot be extended to a certain point of the “sphere.” 相似文献