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1.
We construct irreducible pseudo-Riemannian manifolds (M, g) of arbitrary signature (p, q) with the same curvature tensor as a pseudo-Riemannian symmetric space which is a direct product of a two-dimensional Riemannian space form M 2(c) and a pseudo-Euclidean space with the signature (p, q ? 2), or (p ? 2, q), respectively. 相似文献
2.
3.
Spaces of analytic functions of Hardy-Bloch type 总被引:1,自引:1,他引:0
For 0<p≤∞ and 0<q≤∞, the space of Hardy-Bloch type ℬ(p,q) consists of those functionsf which are analytic in the unit diskD such that (1−r)M
p
(r,f′)⊂L
q
(dr/(1−r)). We note that ℬ(∞,∞) coincides with the Bloch space ℬ and that ℬ⊂ℬ(p,∞) for allp. Also, the space ℬ(p,p) is the Dirichlet spaceD
p−1
p
.
We prove a number of results on decomposition of spaces with logarithmic weights which allow us to obtain sharp results about
the mean growth of the ℬ(p,q). In particular, we prove that iff is an analytic function inD and 2≤p<∞, then the conditionM
p
(r,f′)=O((1−r)−1), asr→1, implies that
. This result is an improvement of the well-known estimate of Clunie and MacGregor and Makarov about the integral means of
Bloch functions, and it also improves the main result in a recent paper by Girela and Peláez. We also consider the question
of characterizing the univalent functions in the spaces ℬ(p,2), 0<p<∞, and in some other related spaces and give some applications of our estimates to study the Carleson measures for the spaces
ℬ(p,2) andD
p−1
p
.
The first and third authors were supported by grants from “E1 Ministerio de Educación y Ciencia”, Spain (MTN2004-00078 and
MTN2004-21420-E) and by a grant from “La Junta de Andalucía” (FQM-210).
The second author was supported in part by MNZŽS Grant, No. ON144010, Serbia. 相似文献
4.
Let C → M be the bundle of connections of a principal G-bundle P → M over a pseudo-Riemannian manifold (M,g) of signature (n+, n−) and let E → M be the associated bundle with P under a linear representation of G on a finite-dimensional vector space. For an arbitrary Lie group G, the O(n+, n−) × G-invariant quadratic Lagrangians on J1(C × M E) are characterized. In particular, for a simple Lie group the Yang–Mills and Yang–Mills–Higgs Lagrangians are characterized,
up to an scalar factor, to be the only O(n+, n−) × G-invariant quadratic Lagrangians. These results are also analyzed on several examples of interest in gauge theory.
Submitted: May 19, 2005; Accepted: April 25, 2006 相似文献
5.
Some infinite family is constructed of orientable three-dimensional closed manifoldsM
n
(p, q), where n ≥ 2, p ≥ 3, 0 < q < p, and (p, q) = 1, such that M
n
(p, q) is an n-fold cyclic covering of the lens space L(p, q) branched over a two-component link. 相似文献
6.
In this article, we study the boundedness of pseudo-differential operators with symbols in S
ρ,δ
m
on the modulation spaces M
p,q
. We discuss the order m for the boundedness Op(S
ρ,δ
m
)⊂ℒ(M
p,q
) to be true. We also prove the existence of a Calderón-Zygmund operator which is not bounded on the modulation space M
p,q
with q≠2. This unboundedness is still true even if we assume a generalized T(1) condition. These results are induced by the unboundedness of pseudo-differential operators on M
p,q
whose symbols are of the class S
1,δ
0 with 0<δ<1.
相似文献
7.
Zhang Shuna 《Advances in Applied Clifford Algebras》2005,15(2):233-238
In this paper, the concepts of Lorentz inner product with (p, q) form, the Lorentz space and the Lorentz transformation with (p, q) form are given by using Clifford algebra. It is shown that Lmp,q is the Lorentz transformation with (p, q) form, and the matrix equality relation of Minkowski space with (n − 1, 1) form is given. The examples are given to illustrate the corresponding results. 相似文献
8.
This paper contains a study of the structure of the Fréchet space L
p
−, 1< p ≤∞, defined as the intersection of L
q
[0,1] for q<p, and endowed with the projective topology. The main topics covered are: normable, Schwartz and nuclear subspaces of L
p
−; construction of uncomplemented copies of ?2 inside L
p
− for p<2; construction of Montel non-Schwartz subspaces; the space L
p
− is primary.
Received: 30 October 1996 / Revised version: 1 February 1998 相似文献
9.
Assuming m − 1 < kp < m, we prove that the space C
∞(M, N) of smooth mappings between compact Riemannian manifolds M, N (m = dim M) is dense in the Sobolev space W
k,p
(M, N) if and only if π
m−1(N) = {0}. If π
m−1(N) ≠ {0}, then every mapping in W
k,p
(M, N) can still be approximated by mappings M → N which are smooth except in finitely many points. 相似文献
10.
Novica Bla?i? 《Differential Geometry and its Applications》2006,24(6):563-566
Let M be a pseudo-Riemannian manifold of signature (p,q) where p?1 and q?1. If the Jacobi operator has pointwise bounded spectrum on the pseudo-sphere bundles of unit spacelike or timelike vectors, then M is pointwise Osserman. Similar results are established for other natural operators of Riemannian geometry. Rigidity phenomena in Lorentzian geometry are discussed. 相似文献
11.
Atsushi Tachikawa 《manuscripta mathematica》1992,74(1):69-81
In this paper we show a nonexistence result for harmonic maps with a rotational nondegeneracy condition from a Riemannian
manifoldM with polep
0 to a negatively curved Hadamard manifold under the condition that the metric tensor ofM is bounded and that the sectional curvature ofM at a pointp is bounded from below by −c dist(p
0,p)−2 (c: a positive constant) as dist(p
0,p)→∞.
Partly supported by Grants-in-Aid for Scientific Research, The Ministry of Education, Science and Culture, Japan 相似文献
12.
This work examines the existence of (4q
2,2q
2−q,q
2−q) difference sets, for q=p
f
, where p is a prime and f is a positive integer. Suppose that G is a group of order 4q
2 which has a normal subgroup K of order q such that G/K
≅
C
q
×C
2×C
2, where C
q
,C
2 are the cyclic groups of order q and 2 respectively. Under the assumption that p is greater than or equal to 5, this work shows that G does not admit (4q
2,2q
2−q,q
2−q) difference sets. 相似文献
13.
Let G = ℤ
p
, p an odd prime, act freely on a finite-dimensional CW-complex X with mod p cohomology isomorphic to that of a lens space L
2m−1(p; q
1, …, q
m
). In this paper, we determine the mod p cohomology ring of the orbit space X/G, when p
2 ∤ m. 相似文献
14.
Stephen Montgomery-Smith 《Israel Journal of Mathematics》2002,131(1):51-60
LetX
1,X
2, …,X
n
be a sequence of independent random variables, letM be a rearrangement invariant space on the underlying probability space, and letN be a symmetric sequence space. This paper gives an approximate formula for the quantity ‖‖(X
i
)‖
N
‖
M
wheneverL
q
embeds intoM for some 1≤q<∞. This extends work of Johnson and Schechtman who tackled the case whenN=ℓ
p
, and recent work of Gordon, Litvak, Schütt and Werner who obtained similar results for Orlicz spaces.
The author was partially supported by NSF grant DMS 9870026, and a grant from the Research Office of the University of Missouri. 相似文献
15.
Jan Peleska 《Aequationes Mathematicae》1984,27(1):20-31
Generalizing theorems of Myers-Steenrod and of Hawking, we obtain characterizations for isometries and conformal mappings of pseudo-Riemannian spaces (M, g): Define a local distance function on convex normal neighbourhoods by (p, q) =g(exp
p
–1
q, exp
p
–1
q). Then every homeomorphismf locally preserving these functions is an isometry. If (M, g) has indefinite signature andf locally preserves distance zero, it is a conformal diffeomorphism. 相似文献
16.
This paper, self-contained, deals with pseudo-unitary spin geometry. First, we present pseudo-unitary conformal structures
over a 2n-dimensional complex manifold V and the corresponding projective quadrics
for standard pseudo-hermitian spaces Hp,q. Then we develop a geometrical presentation of a compactification for pseudo-hermitian standard spaces in order to construct
the pseudo-unitary conformal group of Hp,q. We study the topology of the projective quadrics
and the “generators” of such projective quadrics. Then we define the space S of spinors canonically associated with the pseudo-hermitian scalar product of signature (2n−1, 2n−1). The spinorial group Spin U(p,q) is imbedded into SU(2n−1, 2n−1). At last, we study the natural imbeddings of the projective quadrics
相似文献
17.
Frederic Palesi 《Geometriae Dedicata》2011,151(1):107-140
Let M be a non-orientable surface with Euler characteristic χ(M) ≤ −2. We consider the moduli space of flat SU(2)-connections, or equivalently the space of conjugacy classes of representations
\mathfrakX (M) = Hom (p1 (M), SU (2)) / SU (2).\mathfrak{X} (M) = {\rm Hom} (\pi_1 (M), {\rm SU} (2)) / {\rm SU} (2). 相似文献
18.
Huashui Zhan 《Applications of Mathematics》2008,53(6):521-533
We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation u
t
= div(u
m−1|Du|
p−2
Du) − u
q
with an initial condition u(x, 0) = u
0(x). Here the exponents m, p and q satisfy m + p ⩾ 3, p > 1 and q > m + p − 2.
The paper was supported by NSF of China (10571144), NSF for youth of Fujian province in China (2005J037) and NSF of Jimei
University in China. 相似文献
19.
David Gilat 《Israel Journal of Mathematics》1988,63(3):270-280
For eachp>1, the supremum,S, of the absolute value of a martingale terminating at a random variableX inL
p, satisfiesES≦(Γ(q))1/q‖X‖p (q=p(p-1)-1).The maximum,M, of a mean-zero martingale which starts at zero and terminates atX, satisfiesES≦(Γ(q))1/q‖X‖p (q=p(p-1)-1), whereσ
q is the unique solution of the equationt = ‖Z −t ‖
q
for an exponentially distributed random variableZ with mean 1.σ
p has other characterizations and satisfies lim
p‖
q
− 1
σ
q =c withc determined byce
c+1 = 1. Equalities in (1) and (2) are attainable by appropriate martingales which can be realized as stopped segments of Brownian
motion. A presumably new property of the exponential distribution is obtained en route to inequality (2). 相似文献
20.
Given a submanifold M
n
of Euclidean space ℝ
n
+
p
with codimension p≤6, under generic conditions on its second fundamental form, we show that any other isometric immersion of M
n
into ℝ
n
+
p
+
q
, 0≤q≤n− 2p−1 and 2q≤n+ 1 if q≥ 5, must be locally a composition of isometric immersions. This generalizes several previous results on rigidity and compositions
of submanifolds. We also provide conditions under which our result is global.
14 March 2001 相似文献
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