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1.
We consider immersions: and construct a subspace of which corresponds to a set of embedded manifolds which are either parallel to f, tubes around f or, in general, partial tubes around f. This space is invariant under the action of the normal holonomy group, We investigate the case where is non-trivial and obtain some results on the number of connected components of .
Received 24 March 2000. 相似文献
2.
We define the equivariant holonomy of an invariant connection on a principal -bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant -bundles with connection are shown to be classified by its equivariant holonomy modulo isomorphisms. We also show that the equivariant holonomy can be used to obtain results about equivariant prequantization and anomaly cancellation. 相似文献
3.
对于独立同分布随机变量序列{Xn,n≥1},证明了其满足弱大数律的一个必要条件是:对于任何r∈(0,1),E|X|r<∞都成立.另外我们还举例说明了这样的条件不是充分的. 相似文献
4.
Let X be a closed, oriented Riemannian 4-manifold. Suppose that a cyclic group Z(
p
(p is prime) acts on X by an orientation preserving isometry with an embedded Riemann surface as fixed point set. We study the representation of Z
p
on the Spinc-bundles and the Z
p-invariant moduli space of the solutions of the Seiberg–Witten equations for a Spinc-structure X. When the Z
p
action on the determinant bundle det L acts non-trivially on the restriction L| over the fixed point set , we consider -twisted solutions of the Seiberg-Witten equations over a Spinc-structure ' on the quotient manifold X/Z
p
X', (0,1). We relate the Z
p
-invariant moduli space for the Spinc-structure on X and the -twisted moduli space for the Spinc-structure on X'. From this we induce a one-to-one correspondence between these moduli spaces and calculate the dimension of the -twisted moduli space. When Z
p
acts trivially on L|, we prove that there is a one-to-one correspondence between the Z
p
-invariant moduli space M(
Zp
and the moduli space M (") where ' is a Spinc-structure on X' associated to the quotient bundle L/Z
p
X'. vskip0pt When p = 2, we apply the above constructions to a Kahler surface X with b
2
+
(X) > 3 and H
2(X;Z) has no 2-torsion on which an anti-holomorphic involution acts with fixed point set , a Lagrangian surface with genus greater than 0 and []2H
2(H ;Z). If
K
X
2 > 0 or K
X
2
= 0 and the genus g()> 1, we have a vanishing theorem for Seiberg–Witten invariant of the quotient manifold X'. When K
X
2
= 0 and the genus g()= 1, if there is a Z
2-equivariant Spinc-structure on X whose virtual dimension of the Seiberg–Witten moduli space is zero then there is a Spinc-structure " on X' such that the Seiberg-Witten invariant is ±1. 相似文献
5.
We build examples of Norden metrics on × S
1, where R
2 n
n
is either a pseudosphere or a pseudohyperbolic space. These turn out to be locally conformal to flat anti-Kählerian metrics, strongly non anti-Kählerian, and with a parallel Lee form. Conversely, any connected complete anti-Hermitian manifold possessing these properties is shown to be locally analytically homothetic to × S
1. 相似文献
6.
Ya. V. Bazaikin 《Siberian Mathematical Journal》2007,48(1):8-25
We construct some complete Spin(7)-holonomy Riemannian metrics on the noncompact orbifolds that are ?4-bundles with an arbitrary 3-Sasakian spherical fiber M. We prove the existence of the smooth metrics for M = S 7 and M = SU(3)/U(1) which were found earlier only numerically. 相似文献
7.
McKenzie Y. Wang 《Annals of Global Analysis and Geometry》1995,13(1):31-42
We examine the possibilities of the full holonomy groups of locally irreducible but not necessarily complete Riemannian spin manifolds admitting a non-trivial parallel spinor and discuss some applications of this classification.partially supported by NSERC Grant No. OPG0009421 相似文献
8.
We give a necessary and sufficient condition for a submanifold with parallel focal structure to give rise to a global foliation of the ambient space by parallel and focal manifolds. We show that this is a singular Riemannian foliation with complete orthogonal transversals. For this object we construct an action on the transversals that generalizes the Weyl group action for polar actions.
9.
The generalization of geometric phase for the quantum systems described by quaternionic quantum mechanics is given. The geometry of the quantum cyclic evolution is studied and the quaternionic Berry phase is shown to be given by the holonomy of the suitably defined fiber bundle. 相似文献
10.
In an abstract Wiener space setting, we construct a rigorous mathematical model of the one-loop approximation of the perturbative Chern–Simons integral, and derive its explicit asymptotic expansion for stochastic Wilson lines. 相似文献