共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we define closed partially conformal vector fields and use them to give a characterization of Riemannian manifolds
which admit this kind of fields as some special warped products foliated by (n − 1)-umbilical hypersurfaces. Examples are described in space forms. In particular, closed partially conformal vector fields
in Euclidean spaces are associated to the most simple foliations given by hyperspheres, hyperplanes or coaxial cylinders.
Finally, for manifolds admitting such vector fields, we impose conditions for a hypersurface to be (n − 1)-umbilical, or, in particular, a leaf of the corresponding foliation. 相似文献
2.
On the Construction of <Emphasis Type="Italic">p</Emphasis>-Harmonic Morphisms and Conformal Actions
Xiao Huan MO Li Bing HUANG Yuan Zheng ZHANG 《数学学报(英文版)》2007,23(8):1475-1484
We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce p-harmonic morphisms. By using this criterion we manufacture conformal foliations, with codimension not equal to p, which are locally the fibres of p-harmonic morphisms. Then we give a new approach for the construction of p-harmonic morphisms from R^m/{0} to R^n. By the well-known representation of Clifford algebras, we find an abundance of the new 2/3 (m + 1)-harmonic morphism Ф: R^m/{0} → R^n where m = 2κδ(n - 1). 相似文献
3.
Kazumi Tsukada 《Geometriae Dedicata》1997,68(1):61-71
We investigate holomorphic maps between compact generalized Hopf manifolds (i.e., locally conformal Kähler manifolds with parallel Lee form). We show that they preserve the canonical foliations. Moreover, we study compact complex submanifolds of g.H. manifolds and holomorphic submersions from compact g.H. manifolds. 相似文献
4.
We prove \(h\) -principle for locally conformal symplectic foliations and contact foliations on open manifolds. We then interpret the results in terms of regular Jacobi structures on manifolds. 相似文献
5.
We study transverse conformal Killing forms on foliations and prove a Gallot–Meyer theorem for foliations. Moreover, we show that on a foliation with C-positive normal curvature, if there is a closed basic 1-form ${\phi}$ such that ${\Delta_B\phi=qC\phi}$ , then the foliation is transversally isometric to the quotient of a q-sphere. 相似文献
6.
Alcides Lins Neto 《Bulletin of the Brazilian Mathematical Society》2012,43(1):129-169
The Baum-Bott map associates to a foliation the Baum-Bott indexes of their singularities. In this paper we study the fibers
of the Baum-Bott map in the space of foliations of degree two on the projective plane ℙ2. In the main result we prove that its generic fiber contains exactly 240 orbits of the natural action of Aut(ℙ2) onthespace of foliations. 相似文献
7.
In this article, we show that the Newton transformations of the shape operator can be applied successfully to foliated manifolds.
Using these transformations, we generalize known integral formulae (due to Brito–Langevin–Rosenberg, Ranjan, Walczak, etc.)
for foliations of codimension one. We obtain integral formulae involving rth mean curvature of the second fundamental form of a foliation, the Jacobi operator in the direction orthogonal to the foliation,
and their products. We apply our formulae to totally umbilical foliations and foliations whose leaves have constant second
order mean curvature. 相似文献
8.
9.
We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversally
conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group. We prove
that either there exists a measure invariant under all the elements of the group (or the pseudo-group), or almost surely a
long composition of maps contracts a ball exponentially. We deduce some results about the unique ergodicity.
Received: June 2005, Revision: January 2006, Accepted: March 2006 相似文献
10.
The aim of this article is to give a new dynamical proof of the Ferrand–Obata theorem when the manifold is compact. This will give us a generalisation of this theorem to transversally conformal foliations ofcodimension greater than three and constant basic functions. 相似文献
11.
The main purpose of the present paper is to study geometric properties of transversal (infinitesimal) harmonic transformations for Riemannian foliations. For the point foliation these notions are discussed in [14]. Especially we treat transversal infinitesimal harmonic transformations from the standpoint of λ-automorphisms. Our results extend those obtained in
[6, 7, 15] for the case of harmonic foliations.
Mathematics Subject Classifications (2000): Primary 53C20, Secondary 57R30. 相似文献
12.
Luís Gustavo Mendes 《Geometriae Dedicata》2009,139(1):33-47
The idea of the proof of the classical Noether–Fano inequalities can be adapted to the domain of codimension one singular
holomorphic foliations of the projective space. We obtained criteria for proving that the degree of a foliation on the plane
is minimal in the birational class of the foliation and for the non-existence of birational symmetries of generic foliations
(except automorphisms). Moreover, we give several examples of birational symmetries of special foliations illustrating our
results.
相似文献
13.
In this article, we prove that various classical conformal diffeomorphism groups, which are known to be essential (Banyaga,
J Geom 68(1–2):10–15, 2000), are in fact properly essential. This is a consequence of a local criterion on a conformal diffeomorphism in the form of
a cohomological equation. Furthermore, we study the orbit of a tensor field under the action of the conformal diffeomorphism
group for these classical conformal structures. On every closed contact manifold, we find conformal contact forms that are
not diffeomorphic. 相似文献
14.
In this short note we continue our study of Koszul-Vinberg algebroids which form a subcategory of the category of Lie algebroids, and which appear naturally in the study of affine structures, affine and transversally affine foliations [N. Nguiffo Boyom, R. Wolak, J. Geom. Phys. 42 (2002) 307-317]. We prove a local decomposition theorem for KV-algebroids. Using the notion of KV-algebroids we introduce a new class of singular foliations: affine singular foliations. In the last section we study the holonomy of these foliations and prove a stability theorem. 相似文献
15.
D. S. Volk 《Journal of Mathematical Sciences》2008,150(5):2326-2334
In this paper, we prove that in the space of polynomial foliations of a fixed degree of the complex two-dimensional space,
foliations with separatrix connection, i.e., foliations in which any two distinct points have a common separatrix, are dense.
The main tool of the proof is the analysis of the monodromy group of the foliation in a neighborhood of the infinitely distant
point of the ambient projective space.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 53–64, 2006. 相似文献
16.
17.
In this article, we generalize known integral formulae (due to Brito–Langevin–Rosenberg, Ranjan and the second author) for
foliations of codimension 1 or unit vector fields and obtain an infinite series of such formulae involving invariants of the
Weingarten operator of a unit vector field, of the Jacobi operator in its direction, and their products. We write several
such formulae explicitly, on locally symmetric spaces as well as on arbitrary Riemannian manifolds where they involve also
covariant derivatives of the Jacobi operator. We work also with foliations of codimension 1 (or vector fields) which admit
“good” (in a sense) singularities. 相似文献
18.
In this paper we study (smooth and holomorphic) foliations which are invariant under transverse actions of Lie groups.
Authors’ address: Alexandre Behague and Bruno Scárdua, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa
Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil 相似文献
19.
Sergey Ivashkovich 《Geometric And Functional Analysis》2011,21(1):70-140
The purpose of this paper is the study of vanishing cycles in holomorphic foliations by complex curves on compact complex
manifolds. The main result consists in showing that a vanishing cycle comes together with a much richer complex geometric
object – we call this object a foliated shell. 相似文献
20.
In this paper we study the complex basic cohomology of transversely Hermitian foliations. We use the methods developed in [7] and prove that for transversely Kähler foliations the foliated version of the Frölicher spectral sequence collapses at the first level and that the minimal model for the complex basic cohomology is formal. To stress that these properties are particular to transversely Kähler foliations we construct examples of transversely Hermitian foliations for which these theorems do not hold. 相似文献