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1.
Qiaoling Wang 《Annals of Global Analysis and Geometry》2004,25(1):1-9
We show that a complete noncompact n-dimensional Riemannian manifold Mwith Ricci curvature Ric
M
–(n – 1) and conjugateradius conj
M
c > 0 has finite topological type, provided that the volume growth of geodesic balls in M is not very far from that of the balls in an n-dimensional hyperbolic space H
n
(–1)of sectional curvature –1. We also show that a complete open Riemannian manifold M with nonnegative intermediate Ricci curvature and quadratic curvature decay has finite topological typeif the volume of geodesic balls of M around the base point grows slowly. 相似文献
2.
Frank Leitenberger 《Mathematische Nachrichten》1994,169(1):185-205
The method of coadjoint orbits is developed for the group of real analytic germs of diffeomorphisms φ with φ(0) = 0 and φ′(0) = 1. The form of all infinite dimensional coadjoint orbits is described. Classes U of unitary representations are constructed. In the case n = 2 these representations are related to coadjoint orbits. 相似文献
3.
We show that the complexity of the Voronoi diagram of a collection of disjoint
polyhedra in general position in 3-space that have n vertices overall, under a
convex distance function induced by a polyhedron with O(1) facets, is
O(n
2+), for any > 0. We also show that when the sites are n
segments in 3-space, this complexity is O(n
2 (n) log n). This
generalizes previous results by Chew et al. and by Aronov and
Sharir, and solves an open problem put forward by Agarwal and
Sharir. Specific distance functions for which our results hold are
the L
1 and L
\infty metrics. These results imply that we can preprocess a
collection of polyhedra as above into a near-quadratic data structure that can
answer -approximate Euclidean nearest-neighbor queries amidst the polyhedra
in time O(log (n/) ), for an arbitrarily small > 0. 相似文献
4.
Cordero Luis A. Fernández Marisa Ugarte Luis 《Annals of Global Analysis and Geometry》2002,22(4):355-373
For any compact complex manifold M with a compatible symplectic form, we consider the homomorphisms L
1,0: H
1,0(M) H
{n, n–1(M) and L
0, 1: H
0, 1(M) H
n – 1, n
(M) given by the cup product with []
n – 1, n being the complex dimension of M andH
*, *(M) the Dolbeault cohomology of M. We say that Mhas Lefschetz complex type (1, 0) (resp. (0, 1)) if L
1, 0 (resp.L
0, 1) is injective. Such conditions can be considered as complexversions of the (real) Lefschetz condition studied by Benson and Gordonin [Topology
27 (1988), 513–518]for symplectic manifolds. Within the class of compactcomplex nilmanifolds, we prove that the injectivity of L
1, 0characterizes those complex structures which are Abelian in the sense ofBarberis et al. [Ann. Global Anal. Geom.
13 (1995), 289–301]. In contrast, complex tori are the only nilmanifolds having Lefschetz complex type (0, 1). 相似文献
5.
Seongtag Kim 《Geometriae Dedicata》1997,64(3):373-381
We let (M,g) be a noncompact complete Riemannian manifold of dimension n 3 whose scalar curvature S(x) is positive for all x in M. With an assumption on the Ricci curvature and scalar curvature at infinity, we study the behavior of solutions of the Yamabe equation on –u+[(n–2)/(4(n–1))]Su=qu
(n+2)/(n–2) on (M,g). This study finds restrictions on the existence of an injective conformal immersion of (M,g) into any compact Riemannian n -manifold. We also show the existence of a complete conformal metric with constant positive scalar curvature on (M,g) with some conditions at infinity. 相似文献
6.
V. Z. Grines E. Ya. Gurevich V. S. Medvedev 《Proceedings of the Steklov Institute of Mathematics》2010,270(1):57-79
Let M
n
be a closed orientable manifold of dimension n > 3. We study the class G
1(M
n
) of orientation-preserving Morse-Smale diffeomorphisms of M
n
such that the set of unstable separatrices of any f ∈ G
1(M
n
) is one-dimensional and does not contain heteroclinic intersections. We prove that the Peixoto graph (equipped with an automorphism)
is a complete topological invariant for diffeomorphisms of class G
1(M
n
), and construct a standard representative for any class of topologically conjugate diffeomorphisms. 相似文献
7.
N. V. Ivanov 《Journal of Mathematical Sciences》1984,26(1):1646-1664
The goal of the paper is to calculate the homotopy type of the space of diffeomorphisms for most orientable three-dimensional manifolds with finite fundamental group containing the Klein bottle. The fundamental group of such a manifold Q has the form <a, b ¦abab
–1=1,a
mb2n=1>. As m and n one can have any relatively prime natural numbers; these numbers m, n determine the manifold Q up to diffeomorphism. Let K be a Klein bottle lying in Q and let P be a closed tubular neighborhood in Q of this Klein bottle K. We denote by Diffo(Q) the connected component of the space of diffeomorphisms QQ containing id Q, and by E0(K, Q) the connected component of the space of imbeddings KQ containing the inclusion KQ; analogously we define E0(K, P). The main results of the paper are the following two theorems. THEOREM 1. If m, n1, then the space Diffo(Q) is homotopy equivalent with a circle. THEOREM 2. If m, n1, then the inclusion E0(K, P) E0(K, Q) is a homotopy equivalence. With the help of familiar results on spaces of diffeomorphisms of irreducible manifolds which are sufficiently large, Theorem 1 reduces without difficulty to Theorem 2. The main difficulty is the proof of Theorem 2. This proof develops a technique of Hatcher and the author which deals with spaces of PL-homeomorphisms and diffeomorphisms of irreducible manifolds which are sufficiently large. In the paper we use a different structure definition of the class of manifolds considered. It is easy to verify that these definitions are equivalent.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 122, pp. 72–103, 1982. 相似文献
8.
Mikhail Verbitsky 《Geometric And Functional Analysis》1996,6(4):601-611
We announce the structure theorem for theH
2(M)-generated part of cohomology of a compact hyperkähler manifold. This computation uses an action of the Lie algebra so(4,n–2) wheren=dimH
2(M) on the total cohomology space ofM. We also prove that every two points of the connected component of the moduli space of holomorphically symplectic manifolds can be connected with so-called twistor lines — projective lines holomorphically embedded in the moduli space and corresponding to the hyperkähler structures. This has interesting implications for the geometry of compact hyperkähler manifolds and of holomorphic vector bundles over such manifolds. 相似文献
9.
V. Z. Grines E. Ya. Gurevich V. S. Medvedev 《Proceedings of the Steklov Institute of Mathematics》2008,261(1):59-83
Let M n be a closed orientable manifold of dimension greater than three and G 1(M n ) be the class of orientation-preserving Morse-Smale diffeomorphisms on M n such that the set of unstable separatrices of every f ∈ G 1(M n ) is one-dimensional and does not contain heteroclinic orbits. We show that the Peixoto graph is a complete invariant of topological conjugacy in G 1(M n ). 相似文献
10.
V. A. Yumaguzhin 《Acta Appl Math》2002,72(1-2):155-181
It is known that a linear ordinary differential equation of order n3 can be transformed to the Laguerre–Forsyth form y
(n)=
i=3
n
a
n–i
(x)y
(n–i) by a point transformation of variables. The classification of equations of this form in a neighborhood of a regular point up to a contact transformation is given. 相似文献
11.
Dr. Herbert E. Salzer 《Numerische Mathematik》1971,18(2):144-153
We considern-point Lagrange-Hermite extrapolation forf(x), x>1, based uponf(x
i
),i=1(1)n, –1x
i
1, including non-distinct pointsx
i
in confluent formulas involving derivatives. The problem is to find the pointsx
i
that minimize the factor
in the remainderP
n
(x)f
(n)()/n, –1<<x subject to the condition|P
n
(x)|M, –1x1,2–n+1M2
n
. The solution is significant only when a single set of pointsx
i
suffices for everyx>1. The problem is here completely solved forn=1(1)4. Forn>4 it may be conjectured that there is a single minimal
, 0 rn, whererr(M) is a non-decreasing function ofM, P
n
(–1)=(–1)
n
M, and for 0rn–2, thej-th extremumP
n
(x
e, j
)=(–1)
n–j
M,j=1(1)n–r–1 (except forM=M
r
,r=1(1)n–1, whenj=1(1)n–r). 相似文献
12.
Victor Patrangenaru 《Geometriae Dedicata》1994,50(2):143-164
Ann-dimensional Cartan triple is a triple (g, ,
) consisting of a Lie subalgebra g of so(n) (endowed with the Killing form), a linear map :
n
g and a bilinear antisymmetric map 2(
n
, g), which together satisfy (1.25)–(1.28) of Section 1. LetM
n be the set ofmaximal n-dimensional Cartan triples, and letA
n be thenatural action of the orthogonal group O(n) onM
n (Section 3). One shows that there is a bijective mapping from the set of local isometry classes ofn-dimensional locally homogeneous Riemannian manifolds to the set of orbits ofA
n (Theorem 3.1(a)). Under this bijection, the classes of homogeneous Riemannian manifolds correspond to orbits ofclosed Cartan triples. 相似文献
13.
Peter C. Fishburn 《Order》1999,16(4):335-396
Let M
n
(k) denote the family of posets on n points with k ordered pairs that maximize the number of linear extensions among all such posets. Fishburn and Trotter [2] prove that every poset in M
n
(k) is a semiorder and identifies all semiorders in M
n
(k) for k n. The present paper specifies M
n
(k) for all k 2 n – 3. 相似文献
14.
Catherine M. Bonan-Hamada William B. Jones W. J. Thron Arne Magnus 《Numerical Algorithms》1992,3(1):67-74
On the space, , of Laurent polynomials (L-polynomials) we consider a linear functional which is positive definite on (0, ) and is defined in terms of a given bisequence, {
k
}
–
. Two sequences of orthogonal L-polynomials, {Q
n
(z)
0
and
, are constructed which span in the order {1,z
–1,z,z
–2,z
2,...} and {1,z,z
–1,z
2,z
–2,...} respectively. Associated sequences of L-polynomials {P
n
(z)
0
, and
are introduced and we define rational functions
, wherew is a fixed positive number. The partial fraction decomposition and integral representation of,M
n
(z, w) are given and correspondence of {M
n
(z, w)} is discussed. We get additional solutions to the strong Stieltjes moment problem from subsequences of {M
n
(z, w)}. In particular when {
k
}
–
is a log-normal bisequence, {M
2n
(z, w)} and {M
2n+1
(z, w)} yield such solutions.Research supported in part by the National Science Foundation under Grant DMS-9103141. 相似文献
15.
Lars Schäfer 《Annals of Global Analysis and Geometry》2007,32(2):125-145
In this paper we study para-tt *-bundles (TM, D, S) on the tangent bundle of an almost para-complex manifold (M, τ). We characterise those para-tt *-bundles with ${\nabla=D + S}In this paper we study para-tt
*-bundles (TM, D, S) on the tangent bundle of an almost para-complex manifold (M, τ). We characterise those para-tt
*-bundles with induced by the one-parameter family of connections given by and prove a uniqueness result for solutions with a para-complex connection D. Flat nearly para-K?hler manifolds and special para-complex manifolds are shown to be such solutions. We analyse which of
these solutions admit metric or symplectic para-tt
*-bundles. Moreover, we give a generalisation of the notion of a para-pluriharmonic map to maps from almost para-complex manifolds
(M, τ) into pseudo-Riemannian manifolds and associate to the above metric and symplectic para-tt
*-bundles generalised para-pluriharmonic maps into , respectively, into SO
0(n,n)/U
π(C
n
), where U
π(C
n
) is the para-complex analogue of the unitary group.
相似文献
16.
M will be a compact connected n-dimensional Riemannian manifold. If M contains a closed connected k-dimensional, 2 k < n, minimal immersed submanifold of M, we define the kth isoperimetric number of M, Ñ
k
(M), as the infimum of the volumes of all such submanifolds. We obtain a number of interesting estimates for Ñ
k
(M), for both general and special manifolds, which appear to be new.Next we turn to isometric actions and a 1931 theorem of M. H. A. Newman involving the size of orbits of group actions on manifolds. We introduce the higher Newman numbers N
k
(M), 1 k n. Roughly speaking, if M admits isometric actions of compact connected Lie groups with k-dimensional principal orbits, N
k
(M) is defined as the infimum over all such actions of the maximum volume of all maximal dimensional orbits. We observe that N
k
(M) Ñ
k
(M), 2 k < n, provided N
k
(M) is defined; hence our prior estimates for the isoperimetric numbers of M apply directly to the higher Newman numbers.As a best possible candidate we conjecture that N
k
(M) vol S
k
(i(M)/), 1 k n, where i(M) denotes the radius of injectivity of M and S
k
(i(M)/) denotes the standard k-sphere of radius i(M)/. We verify the conjecture for various special cases. We conclude the paper by studying Newman's theorem for compact connected Lie groups with invariant metrics and obtaining a lower bound for the size of small subgroups. 相似文献
17.
Elisabetta Barletta 《Annals of Global Analysis and Geometry》2002,22(2):99-118
We study CR submanifolds M in a Hopf manifold (C
H
N
(), J
0, g
0) with the Boothby metric g
0,of maximal CR dimension. Any such M is a CR manifold ofhypersurface type, although embedded in higher codimension, and itsanti-invariant distribution H(M) is spanned by a unit vectorfield U. We classify the CR submanifolds M for which = –J
0
Uis parallel in the normal bundle under assumptions on thespectrum of the Weingarten operator a
. We show that (1) ifa
(U) = (1/2)A (where A is the anti-Lee vector) andM fibres in tori over a CR submanifold of the complex projectivespace, then M lies on the (total space of the) pullback of the Hopf fibration via S C
P
N – 1, for some geodesic hypersphere S, and (2) if a
(U)= 0 and Spec(a
) = {0, c}, for some c R {0}, then M is locally a Riemannian product of totally geodesicsubmanifolds. 相似文献
18.
We study codimension 2 homogeneous submanifolds of Euclidean space for which the index of minimum relative nullity is small. We prove that if minxMf(x)n-5, where (x) denotes the nullity of the second fundamental form of the immersion f at the point x, then the manifold M
n
is either isometric to a sphere or to a product of two spheres S2×S
n–2
or covered by the Riemannian product S
n–1
×R. As a consequence, we obtain a classification of compact codimension 2 homogeneous submanifolds of dimension at least 5. 相似文献
19.
Let M
n
be the moduli space of spatial polygons with n edges. An open dense subset of M
n
admits a T
n–3 -action, although this action does not extend to M
n
. The action together with a symplectic structure on M
n
naturally defines a convex polytope
n
in
n–3. In this paper, from M
n
, we construct a singular symplectic toric manifold with
n
as the image of the moment map. 相似文献
20.
Summary Forf ( C
n() and 0 t x letJ
n
(f, t, x) = (–1)n
f(–x)f
(n)(t) +f(x)f
(n)
(–t). We prove that the only real-analytic functions satisfyingJ
n
(f, t, x) 0 for alln = 0, 1, 2, are the exponential functionsf(x) = c e
x,c, . Further we present a nontrivial class of real-analytic functions satisfying the inequalitiesJ
0
(f, x, x) 0 and
0
x
(x – t)n – 1Jn(f, t, x)dt 0 (n 1). 相似文献