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1.
Fix integers n, x, k such that n≥3, k>0, x≥4, (n, x)≠(3, 4) and k(n+1)<(
n
n+x
). Here we prove that the order x Veronese embedding ofP
n
is not weakly (k−1)-defective, i.e. for a general S⊃P
n
such that #(S) = k+1 the projective space | I
2S
(x)| of all degree t hypersurfaces ofP
n
singular at each point of S has dimension (
n
/n+x
)−1− k(n+1) (proved by Alexander and Hirschowitz) and a general F∈| I
2S
(x)| has an ordinary double point at each P∈ S and Sing (F)=S.
The author was partially supported by MIUR and GNSAGA of INdAM (Italy). 相似文献
2.
Bing-Le Wu 《Geometriae Dedicata》1994,50(3):247-250
In this note we prove that for eachn there are only finitely many diffeomorphism classes of compact isoparametric hypersurfaces ofS
n+1 with four distinct principal curvatures. 相似文献
3.
We show that for any simple (2q−1)-knotk, q>1, and any positive integern, the knot #
1
n
k is the fixed-point set of aZ
n
-action onS
2q+1. Further, we show that for many values ofn there are examples of (2q−1)-knots,q≥2, which are the fixed-point sets of inequivalentZ
n
-actions.
This paper was written whilst the first author was in receipt of a Research Grant from the Science Research Council of Great
Britain. 相似文献
4.
We prove that there exist (n − 1)-dimensional compact embedded rotational hypersurfaces with constant scalar curvature (n − 1)(n − 2)S (S > 1) of S
n
other than product of spheres for 4 ≤ n ≤ 6. As a result, we prove that Leite’s Assertion was incorrect.The project is supported by the grant No. 10531090 of NSFC. 相似文献
5.
Vincent Borrelli 《Israel Journal of Mathematics》2001,125(1):221-235
Letn=4 or 8. We prove that any Lagrangian embedding ofS
n − 1 ×S
1 into ℂ
n
has a trivial linking class. We deduce that every embedding ofS
3 ×S
4 into ℂ4 is isotopic to a Lagrangian embedding. This is false ifn = 8. 相似文献
6.
In this paper, we shall give an integral equality by applying the operator □ introduced by S.Y. Cheng and S.T. Yau [7] to
compact spacelike hypersurfaces which are immersed in de Sitter spaceS
1
n+1
(c) and have constant scalar curvature. By making use of this integral equality, we show that such a hypersurface with constant
scalar curvaturen(n−1)r is isometric to a sphere ifr<c.
Research partially Supported by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science and
Culture. 相似文献
7.
Paola Biondi 《Rendiconti del Circolo Matematico di Palermo》1998,47(2):265-276
LetS be a finite planar space such that any two distinct planes intersect in a line. We show thatk≤n
2+1 for anyk-cap ofS, wheren is the order ofS. Moreover, if a (n
2+1)-cap exists inS, a necessary and sufficient condition is provided forS to be embeddable in a 3-dimensional projective space.
Work supported by the National Research Project “Strutture geometriche, Combinatoria e loro applicazioni” of the italian M.U.R.S.T. 相似文献
8.
A hypersurface f : M → Rn+1 in an affine (n+1)-space is called centroaffine if its position vector is always transversal to f*(TM) in Rn+1. In this paper, we establish a general optimal inequality for definite centroaffine hypersurfaces in Rn+1 involving the Tchebychev vector field. We also completely classify the hypersurfaces which verify the equality case of the inequality. 相似文献
9.
Marjatta Näätänen 《Israel Journal of Mathematics》1978,29(4):346-356
LetD andD′ be ring domains inB
n
, withS
n−1 as one boundary component, and let
be a homeomorphism which isK-quasiconformal inD and withf(S
n−1)=S
n−1. According to a result of Gehringf÷S
n−1 admits an extension
which is quasiconformal inB
n
. We find here an upper bound for the dilatation ofg in terms ofn, K, and modD.
This work was started during a visit to Université de Paris, financed by a cultural exchange program between France and Finland. 相似文献
10.
Cesare Parenti 《Annali di Matematica Pura ed Applicata》1972,93(1):359-389
Summary In §1 we study a class of pseudo-differential operators inR
n. In §3 the results obtained in §§1, 2 are applied to study of an elliptic boundary value problem in the exterior of a bounded domain ofR
n for differential operators whose coefficients have a polynomial growth to infinity.
Entrata in Redazione il 23 marzo 1972. 相似文献
11.
In this work we generalize the case of scalar curvature zero the results of Simmons (Ann. Math. 88 (1968), 62–105) for minimal cones in Rn+1. If Mn−1 is a compact hypersurface of the sphere Sn(1) we represent by C(M)ε the truncated cone based on M with center at the origin. It is easy to see that M has zero scalar curvature if and only if the cone base on M also has zero scalar curvature. Hounie and Leite (J. Differential Geom. 41 (1995), 247–258) recently gave the conditions for the ellipticity of the partial differential equation of the scalar curvature.
To show that, we have to assume n ⩾ 4 and the three-curvature of M to be different from zero. For such cones, we prove that, for n ≤slant 7 there is an ε for which the truncate cone C(M)ε is not stable. We also show that for n ⩾ 8 there exist compact, orientable hypersurfaces Mn−1 of the sphere with zero scalar curvature and S3 different from zero, for which all truncated cones based on M are stable.
Mathematics Subject Classifications (2000): 53C42, 53C40, 49F10, 57R70. 相似文献
12.
For a domainU on a certaink-dimensional minimal submanifold ofS
n orH
n, we introduce a “modified volume”M(U) ofU and obtain an optimal isoperimetric inequality forU k
k
ω
k
M (D)
k-1
≤Vol(∂D)
k
, where ω
k
is the volume of the unit ball ofR
k
. Also, we prove that ifD is any domain on a minimal surface inS
+
n
(orH
n, respectively), thenD satisfies an isoperimetric inequality2π A≤L
2+A2 (2π A≤L2−A2 respectively). Moreover, we show that ifU is ak-dimensional minimal submanifold ofH
n, then(k−1) Vol(U)≤Vol(∂U).
Supported in part by KME and GARC 相似文献
13.
Benjamin Weiss 《Israel Journal of Mathematics》1989,66(1-3):364-368
We give a proof of Tucker’s Combinatorial Lemma that proves the fundamental nonexistence theorem: There exists no continuous
map fromB
n toS
n − 1 that maps antipodal points of∂B
n to antipodal points ofS
n − 1. 相似文献
14.
A. Zabrodsky 《Israel Journal of Mathematics》1972,11(3):315-325
The total spaces of principalSU(n−1) bundles overS
2n−1 are classified. The classification ofSp(n−1) bundles overS
4n−1, is studied as well. As an intermediate step the homotopy equivalences ofSU andSp are classified. 相似文献
15.
A. D. Forbes M. J. Grannell T. S. Griggs 《Rendiconti del Circolo Matematico di Palermo》2007,56(1):17-32
In [8], Quattrochi and Rinaldi introduced the idea ofn
−1-isomorphism between Steiner systems. In this paper we study this concept in the context of Steiner triple systems. The main
result is that for any positive integerN, there existsv
0(N) such that for all admissiblev≥v
0(N) and for each STS(v) (sayS), there exists an STS(v) (sayS′) such that for somen>N, S is strictlyn
−1-isomorphic toS′. We also prove that for all admissiblev≥13, there exist two STS(v)s which are strictly 2−1-isomorphic.
Define the distance between two Steiner triple systemsS andS′ of the same order to be the minimum volume of a tradeT which transformsS into a system isomorphic toS′. We determine the distance between any two Steiner triple systems of order 15 and, further, give a complete classification
of strictly 2−1-isomorphic and 3−1-isomorphic pairs of STS(15)s. 相似文献
16.
17.
J. Kenedy Martins 《Bulletin of the Brazilian Mathematical Society》2001,32(1):83-105
The invariants needed to decide when a pair of hypersurfaces ofS
6 orCP
n
are respectivelyG
2-congruent or holomorpic congruent are determined and this result is used to characterize the hypersurfaces of these spaces whose Hopf vector fields are also Killing fields. 相似文献
18.
LetG be a finite group, andS a subset ofG \ |1| withS =S
−1. We useX = Cay(G,S) to denote the Cayley graph ofG with respect toS. We callS a Cl-subset ofG, if for any isomorphism Cay(G,S) ≈ Cay(G,T) there is an α∈ Aut(G) such thatS
α =T. Assume that m is a positive integer.G is called anm-Cl-group if every subsetS ofG withS =S
−1 and | S | ≤m is Cl. In this paper we prove that the alternating groupA
5 is a 4-Cl-group, which was a conjecture posed by Li and Praeger. 相似文献
19.
Franc Forstneric 《Journal of Geometric Analysis》1999,9(1):93-117
Let n > 1 and let
C
n
denote the complex n-dimensional Euclidean space. We prove several jet-interpolation results for nowhere degenerate entire
mappings F:C
n →C
n
and for holomorphic automorphisms of
C
n
on discrete subsets of
C
n.We also prove an interpolation theorem for proper holomorphic embeddings of Stein manifolds into
C
n.For each closed complex submanifold (or subvariety) M ⊂
C
n
of complex dimension m < n we construct a domain Ω ⊂C
n
containing M and a biholomorphic map F: Ω →
C
n
onto
C
n
with J F ≡ 1such that F(M) intersects the image of any nondegenerate entire map G:C
n−m →C
n
at infinitely many points. If m = n − 1, we construct F as above such that
C
n ∖F(M) is hyperbolic. In particular, for each m ≥ 1we construct proper holomorphic embeddings F:C
m →C
m−1
such that the complement
C
m+1 ∖F(C
m
)is hyperbolic. 相似文献
20.
József Beck 《Combinatorica》1983,3(3-4):281-297
LetS be a set ofn non-collinear points in the Euclidean plane. It will be shown here that for some point ofS the number ofconnecting lines through it exceedsc · n. This gives a partial solution to an old problem of Dirac and Motzkin. We also prove the following conjecture of Erdős: If
any straight line contains at mostn−x points ofS, then the number of connecting lines determined byS is greater thanc · x · n.
Dedicated to Paul Erdős on his seventieth birthday 相似文献