共查询到20条相似文献,搜索用时 11 毫秒
1.
Research partially supported by the NSF 相似文献
2.
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
3.
Ezequiel R. Barbosa 《Bulletin des Sciences Mathématiques》2010,134(7):677
Let (Mn,g), n?3, be a smooth closed Riemannian manifold with positive scalar curvature Rg. There exists a positive constant C=C(M,g) defined by mean curvature of Euclidean isometric immersions, which is a geometric invariant, such that Rg?n(n−1)C. In this paper we prove that Rg=n(n−1)C if and only if (Mn,g) is isometric to the Euclidean sphere Sn(C) with constant sectional curvature C. Also, there exists a Riemannian metric g on Mn such that the scalar curvature satisfies the pinched condition
4.
5.
For a supergoup , we study closed -manifolds with positive conformal classes. We use the relative Yamabe invariant from [2] to define the conformal cobordism
relation on the category of such manifolds. We prove that the corresponding conformal cobordism groups are isomorphic to the cobordism groups defined by Stolz in [19]. As a corollary, we show that the conformal concordance relation on positive conformal classes coincides
with the standard concordance relation on positive scalar curvature metrics. Our main technical tools come from analysis and
conformal geometry.
Received: 22 August 2000 / Published online: 5 September 2002 相似文献
6.
We treat n-dimensional compact minimal submanifolds of complex projective space when the maximal holomorphic tangent subspace is (n − 1)-dimensional and we give a sufficient condition for such submanifolds to be tubes over totally geodesic complex subspaces.
Authors’ addresses: Mirjana Djorić, Faculty of Mathematics, University of Belgrade, Studentski trg 16, pb. 550, 11000 Belgrade,
Serbia; Masafumi Okumura, 5-25-25 Minami Ikuta, Tama-ku, Kawasaki, Japan 相似文献
7.
Spacelike hypersurfaces with constant scalar curvature 总被引:1,自引:0,他引:1
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 space S
n
+1
1(c) and have constant scalar curvature. By making use of this integral equality, we show that such a hypersurface with constant
scalar curvature n(n-1)r is isometric to a sphere if r << c.
Received: 18 December 1996 / Revised version: 26 November 1997 相似文献
8.
Let (M, g) be an n-dimensional compact and connected Riemannian manifold of constant scalar curvature. If the sectional curvatures
of M are bounded below by a constant α > 0, and the Ricci curvature satisfies Ric < (n − 1)αδ, δ ≥ 1, then it is shown that
either M is isometric to the n-sphere Sn(α) or else each nonzero eigenvalue λ of the Laplacian acting on the smooth functions of M satisfies the following:
. 相似文献
9.
Hypersurfaces with constant scalar curvature in space forms 总被引:17,自引:0,他引:17
Li Haizhong 《Mathematische Annalen》1996,305(1):665-672
10.
Jongsu Kim 《Mathematische Annalen》1993,297(1):235-251
11.
In this paper, we give a Möbius characterization of submanifolds in real space forms with parallel mean curvature vector fields and constant scalar curvatures, generalizing a theorem of H. Li and C.P. Wang in [LW1].Supported by NSF of Henan, P. R. China 相似文献
12.
David W. Kribs 《Integral Equations and Operator Theory》2001,41(4):426-454
Non-commutative versions of Arveson's curvature invariant and Euler characteristic for a commutingn-tuple of operators are introduced. The non-commutative curvature invariant is sensitive enough to determine if ann-tuple is free. In general both invariants can be thought of as measuring the freeness or curvature of ann-tuple. The connection with dilation theory provides motivation and exhibits relationships between the invariants. A new class of examples is used to illustrate the differences encountered in the non-commutative setting and obtain information on the ranges of the invariants. The curvature invariant is also shown to be upper semi-continuous. 相似文献
13.
Włodzimierz M. Mikulski 《Geometriae Dedicata》1995,54(2):129-136
For any Weil algebraA we establish a bijection between the set of all natural base-extending operators of foliations into foliations on the Weil functor ofA-velocities and the set of all pairs (I, J) of ideals inA withI J. 相似文献
14.
One important problem in Finsler geometry is that of classifying Finsler metrics of scalar curvature. By investigating the second-order differential equation for a class of Randers metrics with isotropic S-curvature, we give a global classification of these metrics of scalar curvature, generalizing a theorem previously only known in the case of locally projectively flat Randers metrics. 相似文献
15.
Qilin Yang 《Differential Geometry and its Applications》2007,25(1):1-7
It is well known there is no non-constant harmonic map from a closed Riemannian manifold of positive Ricci curvature to a complete Riemannian manifold with non-positive sectional curvature. By reducing the assumption on the Ricci curvature to one on the scalar curvature, such vanishing theorem cannot hold in general. This raises the question: “What information can we obtain from the existence of non-constant harmonic map?” This paper gives answer to this problem; the results obtained are optimal. 相似文献
16.
W. M. Mikulski 《Monatshefte für Mathematik》1994,117(1-2):107-119
We prove that forn-manifolds (n3) the sets of all natural operatorsT(T
r*
,T
q*
) andT-TT
r*
, respectively, are free finitely generatedC
(R
r)-modules. We construct explicitly the bases of theC
(R
r)-modules. 相似文献
17.
W. M. Mikulski 《Monatshefte für Mathematik》1995,119(1-2):63-77
LetA be a Weil algebra withp variables. We prove that forn-manifolds (np+2) the set of all natural operatorsT
*T
*
T
A
is a free finitely generated module over a ring canonically dependent onA. We construct explicitly the basis of this module. 相似文献
18.
Complete space-like hypersurfaces with constant scalar curvature 总被引:6,自引:0,他引:6
Ximin Liu 《manuscripta mathematica》2001,105(3):367-377
Let M
n
be a complete space-like hypersurface with constant normalized scalar curvature R in the de Sitter space S
n
+
1
1 and denote . We prove that if the norm square of the second fundamental form of M
n
satisfies , then either and M
n
is a totally umbilical hypersurface; or , and, up to rigid motion, M
n
is a hyperbolic cylinder .
Received: 8 February 2001 / Revised version: 27 April 2001 相似文献
19.
Takuji Sato 《Journal of Geometry》2003,77(1-2):171-183
We show that a 4-dimensional almost Hermitian manifold (M, J, g) is of pointwise constant
anti-holomorphic sectional curvature if and only if (M, J, g) is self-dual with J-invariant Ricci tensor and
K1212 = 0, where K is the complexification of the Riemannian curvature tensor. 相似文献
20.
Takuji Sato 《Journal of Geometry》2004,80(1-2):196-208
We construct non-compact examples of Hermitian manifolds with pointwise constant anti-holomorphic sectional curvature. Our examples are obtained by conformal change of the metric on an open set of the complex space form. 相似文献