共查询到20条相似文献,搜索用时 750 毫秒
1.
Francisco Martín Cabrera 《Monatshefte für Mathematik》2006,148(1):29-50
We study SU(3)-structures induced on orientable hypersurfaces of seven-dimensional manifolds with G2-structure. Taking Gray-Hervella types for both structures into account, we relate the type of SU(3)-structure and the type of G2-structure with the shape tensor of the hypersurface. Additionally, we show how to compute the intrinsic SU(3)-torsion and the intrinsic G2-torsion by means of the exterior algebra. 相似文献
2.
László Verhóczki 《Monatshefte für Mathematik》2004,141(4):323-335
In the present paper we discuss in detail the cohomogeneity one isometric actions of the Lie groups SU(3) × SU(3) and SU(3) on the exceptional compact symmetric spaces G2 and G2/SO(4), respectively. We show that the principal orbits coincide with the tubular hypersurfaces around the totally geodesic singular orbits, and the symmetric spaces G2 and G2/SO(4) can be thought of as compact tubes around SU(3) and P2, respectively. Moreover, we determine the radii of these tubes and describe the shape operators of the principal orbits. Finally, we apply these results to compute the volumes of the two symmetric spaces.The author was partially supported by the Hungarian National Science and Research Foundation OTKA T032478. 相似文献
3.
Zbigniew Olszak 《Periodica Mathematica Hungarica》1996,33(2):105-113
LetM be a 3-dimensional quasi-Sasakian manifold. On such a manifold, the so-called structure function is defined. With the help of this function, we find necessary and sufficient conditions forM to be conformally flat. Next it is proved that ifM is additionally conformally flat with = const., then (a)M is locally a product ofR and a 2-dimensional Kählerian space of constant Gauss curvature (the cosymplectic case), or (b)M is of constant positive curvature (the non cosymplectic case; here the quasi-Sasakian structure is homothetic to a Sasakian structure). An example of a 3-dimensional quasi-Sasakian structure being conformally flat with nonconstant structure function is also described. For conformally flat quasi-Sasakian manifolds of higher dimensions see [O1] 相似文献
4.
Consider a compact Riemannian manifold (M, g) with metric g and dimension n ≥ 3. The Schouten tensor A
g
associated with g is a symmetric (0, 2)-tensor field describing the non-conformally-invariant part of the curvature tensor
of g. In this paper, we consider the elementary symmetric functions {σ
k
(A
g
), 1 ≤ k ≤ n} of the eigenvalues of A
g
with respect to g; we call σ
k
(A
g
) the k-th Schouten curvature function. We give an isometric classification for compact locally conformally flat manifolds which satisfy the conditions: A
g
is semi-positive definite and σ
k
(A
g
) is a nonzero constant for some k ∈ {2, ... , n}. If k = 2, we obtain a classification result under the weaker conditions that σ2(A
g
) is a non-negative constant and (M
n
, g) has nonnegative Ricci curvature. The corresponding result for the case k = 1 is well known. We also give an isometric classification for complete locally conformally flat manifolds with constant
scalar curvature and non-negative Ricci curvature.
Udo Simon: Partially supported by Chinese-German cooperation projects, DFG PI 158/4-4 and PI 158/4-5, and NSFC. 相似文献
5.
In this paper, we describe the structure of Riemannian manifolds with a special kind of Codazzi spinors. We use them to construct
globally hyperbolic Lorentzian manifolds with complete Cauchy surface for any weakly irreducible holonomy representation with
parallel spinors, t.m. with a holonomy group , where is trivial or a product of groups SU(k), Sp(l), G
2 or Spin (7).
相似文献
6.
Sharp estimates for the Ricci curvature of a submanifold M
n
of an arbitrary Riemannian manifold N
n+p
are established. It is shown that the equality in the lower estimate of the Ricci curvature of M
n
in a space form N
n+p
(c) is achieved only when M
n
is quasiumbilical with a flat normal bundle. In the case when the codimension p satisfies 1 ≤ p ≤ n − 3, the only submanifolds in N
n+p
(c) on which the Ricci curvature is minimal are the conformally flat ones with a flat normal bundle.
相似文献
7.
Lorenz J. Schwachhöfer 《Geometriae Dedicata》1996,62(2):193-208
In Proc. Symp. Pure Math.
53 (1991), 33–88, Bryant gave examples of torsion free connections on four-manifolds whose holonomy is exotic, i.e. is not contained on Berger's classical list of irreducible holonomy representations. The holonomy in Bryant's examples is the irreducible four-dimensional representation of S1(2, #x211D;) (G1(2, #x211D;) resp.) and these connections are called H
3-connections (G
3-connections resp.).In this paper, we give a complete classification of homogeneous G
3-connections. The moduli space of these connections is four-dimensional, and the generic homogeneous G
3-connection is shown to be locally equivalent to a left-invariant connection on U(2). Thus, we prove the existence of compact manifolds with G
3-connections. This contrasts a result in by Schwachhöfer (Trans. Amer. Math. Soc.
345 (1994), 293–321) which states that there are no compact manifolds with an H
3-connection. 相似文献
8.
We construct examples of exponentially asymptotically cylindrical (EAC) Riemannian 7-manifolds with holonomy group equal to
G
2. To our knowledge, these are the first such examples. We also obtain EAC coassociative calibrated submanifolds. Finally,
we apply our results to show that one of the compact G
2-manifolds constructed by Joyce by desingularisation of a flat orbifold T
7/Γ can be deformed to give one of the compact G
2-manifolds obtainable as a generalized connected sum of two EAC SU(3)-manifolds via the method of Kovalev (J Reine Angew Math 565:125–160, 2003). 相似文献
9.
Lisa DeMeyer 《manuscripta mathematica》2001,105(3):283-310
We study the density of closed geodesics property on 2-step nilmanifolds Γ\N, where N is a simply connected 2-step nilpotent Lie group with a left invariant Riemannian metric and Lie algebra ?, and Γ is a lattice
in N. We show the density of closedgeodesics property holds for quotients of singular, simply connected, 2-step nilpotent Lie
groups N which are constructed using irreducible representations of the compact Lie group SU(2).
Received: 8 November 2000 / Revised version: 9 April 2001 相似文献
10.
László Verhóczki 《Monatshefte für Mathematik》2004,109(1):323-335
In the present paper we discuss in detail the cohomogeneity one isometric actions of the Lie groups SU(3) × SU(3) and SU(3) on the exceptional compact symmetric spaces G2 and G2/SO(4), respectively. We show that the principal orbits coincide with the tubular hypersurfaces around the totally geodesic singular orbits, and the symmetric spaces G2 and G2/SO(4) can be thought of as compact tubes around SU(3) and P2, respectively. Moreover, we determine the radii of these tubes and describe the shape operators of the principal orbits. Finally, we apply these results to compute the volumes of the two symmetric spaces. 相似文献
11.
For an equivariant Morse stratification that contains a unique open stratum, we introduce the notion of equivariant antiperfection,
which means the difference of the equivariant Morse series and the equivariant Poincaré series achieves the maximal possible
value (instead of the minimal possible value 0 in the equivariantly perfect case). We also introduce a weaker condition of
local equivariant antiperfection. We prove that the Morse stratification of the Yang-Mills functional on the space of connections
on a principal G-bundle over a connected, closed, nonorientable surface Σ is locally equivariantly
\mathbbQ{\mathbb{Q}}-antiperfect when G = U(2), SU(2), U(3), SU(3); we propose that the Morse stratification is actually equivariantly
\mathbbQ{\mathbb{Q}}-antiperfect in these cases. Our proposal yields formulas of Poincaré series
PtG(Hom(p1(S),G);\mathbbQ){P_t^G({\rm Hom}(\pi_1(\Sigma),G);\mathbb{Q})} when G = U(2), SU(2), U(3), SU(3). Our U(2), SU(2) formulas agree with formulas proved by T. Baird, who also verified our conjectural U(3) formula. 相似文献
12.
Felipe Leitner 《Differential Geometry and its Applications》2011,29(3):440-462
Almost Einstein manifolds are conformally Einstein up to a scale singularity, in general. This notion comes from conformal tractor calculus. In the current paper we discuss almost Einstein structures on closed Riemannian product manifolds and on 4-manifolds of cohomogeneity one. Explicit solutions are found by solving ordinary differential equations. In particular, we construct three families of closed 4-manifolds with almost Einstein structure corresponding to the boundary data of certain unimodular Lie groups. Two of these families are Bach-flat, but neither (globally) conformally Einstein nor half conformally flat. On products with a 2-sphere we find an exotic family of almost Einstein structures with hypersurface singularity as well. 相似文献
13.
In this paper a method for the resolution of the differential equation of the Jacobi vector fields in the manifold V
1 = Sp(2)/SU(2) is exposed. These results are applied to determine areas and volumes of geodesic spheres and balls.
Work partially supported by DGI (Spain) and FEDER Projects MTM 2004-06015-C02-01 and MTM 2007-65852 (first author) and by
Research Project PGIDIT05PXIB16601PR (second author).
Authors’ addresses: A. M. Naveira, Departamento de Geometría y Topología. Facultad de Matemáticas, Avda. Andrés Estellés,
N1, 46100 – Burjassot, Valencia, Spain; A. D. Tarrío Tobar, E. U. Arquitectura Técnica, Campus A Zapateira. Universidad de
A Coru?a, 15192 – A Coru?a, Spain 相似文献
14.
Jean-Pierre Magnot 《Bulletin des Sciences Mathématiques》2004,128(6):513-529
We give a theorem of reduction of the structure group of a principal bundle P with regular structure group G. Then, when G is in the classes of regular Lie groups defined by T. Robart in [Can. J. Math. 49 (4) (1997) 820-839], we define the closed holonomy group of a connection as the minimal closed Lie subgroup of G for which the previous theorem of reduction can be applied. We also prove an infinite dimensional version of the Ambrose-Singer theorem: the Lie algebra of the holonomy group is spanned by the curvature elements. 相似文献
15.
In this paper we show that there exist mod 2 obstructions to the smoothness of 3-Sasakian reductions of spheres. Specifically,
ifS is a smooth 3-Sasakian manifold obtained by reduction of the 3-Sasakian sphereS
4n−1 by a torus, and if the second Betti numberb
2(S)≥2 then dimS=7, 11, 15, whereas, ifb
2 (S)≥5 then dimS=7. We also show that the above bounds are sharp, in that we construct explicit examples of 3-Sasakian manifolds in the cases
not excluded by these bounds.
During the preparation of this work the authors were partially supported by an NSF grant.
This article was processed by the author using the LATEX style file from Springer-Verlag. 相似文献
16.
We give a classification of 3—dimensional conformally flat contact metric manifolds satisfying: =0(=L
g) orR(Y, Z)=k[(Z)Y–(Y)Z]+[(Z)hY]–(Y)hZ] wherek and are functions. It is proved that they are flat (the non-Sasakian case) or of constant curvature 1 (the Sasakian case). 相似文献
17.
Inspired by the recent work [HHM03], we prove two stability results for compact Riemannian manifolds with nonzero parallel spinors. Our first result says that Ricci flat metrics which also admit nonzero parallel spinors are stable (in the direction of changes in conformal structures) as the critical points of the total scalar curvature functional. Our second result, which is a local version of the first one, shows that any metric of positive scalar curvature cannot lie too close to a metric with nonzero parallel spinor. We also prove a rigidity result for special holonomy metrics. In the case of SU(m) holonomy, the rigidity result implies that scalar flat deformations of Calabi-Yau metric must be Calabi-Yau. Finally we explore the connection with a positive mass theorem of [D03], which presents another approach to proving these stability and rigidity results. Dedicated to Jeff Cheeger for his sixtieth birthday 相似文献
18.
We consider a (2m + 3)-dimensional Riemannian manifold M(ξ r, ηr, g ) endowed with a vertical skew symmetric almost contact 3-structure. Such manifold is foliated by 3-dimensional submanifolds
of constant curvature tangent to the vertical distribution and the square of the length of the vertical structure vector
field is an isoparametric function. If, in addition, M(ξ r, ηr, g ) is endowed with an f -structure φ, M, turns out to be a framed f−CR-manifold. The fundamental 2-form Ω associated with φ is a presymplectic form. Locally, M is the Riemannian product
of two totally geodesic submanifolds, where
is a 2m-dimensional Kaehlerian submanifold and
is a 3-dimensional submanifold of constant curvature. If M is not compact, a class of local Hamiltonians of Ω is obtained. 相似文献
19.
We classify all connected subgroups of SO(2, n) that act irreducibly on ℝ2, n
. Apart from SO
0(2, n) itself these are U(1, n/2), SU(1, n/2), if n even, S
1 · SO(1, n/2) if n even and n ≥ 2, and SO
0(1, 2) for n = 3. Our proof is based on the Karpelevich Theorem and uses the classification of totally geodesic submanifolds of complex
hyperbolic space and of the Lie ball. As an application we obtain a list of possible irreducible holonomy groups of Lorentzian
conformal structures, namely SO
0(2, n), SU(1, n), and SO
0(1, 2). 相似文献
20.
Necdet Güner 《Geometriae Dedicata》1996,63(1):17-23
Let N=G/ be a compact nilmanifold, G a connected, simply connected, nilpotent Lie group with its discrete subgroup and Lie algebra
. Let I* (
) denote the invariant differential forms on
.If I* (
) H* (
) is an injective map, then G is abelian and N is a torus. Furthermore, N has a formal minimal model. If N is an even-dimensional compact nilmanifold, it has a Kähler structure and invariant symplectic structure if and only if I* (
) H* (
) is injective. 相似文献