共查询到20条相似文献,搜索用时 15 毫秒
1.
Gabjin Yun 《Geometriae Dedicata》2002,89(1):133-139
Let M
n
, n 3, be a complete oriented immersed minimal hypersurface in Euclidean space R
n+1. We show that if the total scalar curvature on M is less than the n/2 power of 1/C
s
, where C
s
is the Sobolev constant for M, then there are no L
2 harmonic 1-forms on M. As corollaries, such a minimal hypersurface contains no nontrivial harmonic functions with finite Dirichlet integral and so it has only one end. This implies finally that M is a hyperplane. 相似文献
2.
Marcos Petrúcio Cavalcante Heudson Mirandola Feliciano Vitório 《Journal of Geometric Analysis》2014,24(1):205-222
Let $x:M^{m}\to\bar{M}$ , m≥3, be an isometric immersion of a complete noncompact manifold M in a complete simply connected manifold $\bar{M}$ with sectional curvature satisfying $-k^{2}\leq K_{\bar{M}}\leq0$ , for some constant k. Assume that the immersion has finite total curvature in the sense that the traceless second fundamental form has finite L m -norm. If $K_{\bar{M}}\not\equiv0$ , assume further that the first eigenvalue of the Laplacian of M is bounded from below by a suitable constant. We prove that the space of the L 2 harmonic 1-forms on M has finite dimension. Moreover, there exists a constant Λ>0, explicitly computed, such that if the total curvature is bounded from above by Λ then there are no nontrivial L 2-harmonic 1-forms on M. 相似文献
3.
Luigia Di Terlizzi Jerzy J. Konderak Robert A. Wolak 《Mediterranean Journal of Mathematics》2007,4(3):251-261
We consider a Riemannian manifold with a compatible f-structure which admits a parallelizable kernel. With some additional integrability conditions it is called
-manifold. This class of manifolds is a natural generalization of the Sasakian manifolds. We study properties of harmonic
1-forms on such a manifold and deduce some topological properties.
Research supported by the Italian MIUR 60% and GNSAGA.
Professor J.J. Konderak died just during the preparation of this paper. His contribution has been substantial.
Note of the Editor-in-Chief. Professor Jerzy J. Konderak passed away on September 14, 2005, at the age of 49. Born on February 12, 1956, in Krakow, Poland,
he received his Ph.D. in 1986 from the Jagiellonian University of Krakow.
Since 2003 he was associated professor of Mathematics at the Faculty of Sciences of the University of Bari. The main area
of his scientific interests was Differential Geometry.
Professor Konderak was a very gifted researcher and was appreciated by students and colleagues for his passion and devotion
to Mathematics and its teaching. All the colleagues of the Department of Mathematics of the University of Bari will remember
him not only as a clever mathematician but also as a men of rare quality. 相似文献
4.
本文证明了单位球面中极小子流形的一些拼挤定理,特别注意到单位球面中的极小超曲面、给出了截曲率的拼挤常数,我们也改进了由N.Ejiri得到的Ricci曲率拼挤常数。 相似文献
5.
6.
Let x: L
n
S2n+1 R2n+2 be a minimal submanifold in S2n+1. In this note, we show that L is Legendrian if and only if for any A su(n + 1) the restriction to L of Ax, (–1)x satisfies f = 2(n + 1)f. In this case, 2(n + 1) is an eigenvalue of the Laplacian with multiplicity at least
(n(n + 3)). Moreover if the multiplicity equals to
;(n(n + 3)), then L
n
is totally geodesic. 相似文献
7.
8.
局部对称黎曼流形中的极小子流形 总被引:1,自引:0,他引:1
In this paper, we discuss the compact minimal submanifolds in locally symmetric Riemannian manifolds. Two Pinching theorems are obtained and two corresponding results of Chern, S. S. and Yau S. T. are generalized. 相似文献
9.
在一个类似于稳定不等式的条件下,得到了欧氏空间中完备极小子流形的Bernstein型定理.我们的结果部分推广了Li H.Z.和Wei G.X.的定理. 相似文献
10.
Antonio J. Di Scala 《Annals of Global Analysis and Geometry》2002,21(1):15-18
We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex homogeneous submanifold of C
N
must be totally geodesic. 相似文献
11.
We use the method of H. Gauchman [2] to show that if the sectionalcurvature of a compact minimal n-dimensional submanifold ina unit sphere is everywhere bigger than n/2(n+1) then it mustbe totally geodesic. We also discuss some related results andconjectures. 相似文献
12.
A. Lotta 《Acta Mathematica Hungarica》1999,84(1-2):135-148
Examples of slant submanifolds in the Sasakian space R2n+1 are obtained as the leaves of a harmonic, Riemannian 3-dimensional foliation. With the exception of the anti-invariant ones, these leaves are all locally homogeneous manifolds with negative scalar curvature, whose Ricci tensor satisfies (S)(X, X) = 0 for all tangent vector fields. 相似文献
13.
Qing Chen 《Annals of Global Analysis and Geometry》1998,16(5):413-418
Let M be a properly immersed n-dimensional complete minimal submanifold in Euclidean space Rn+p of dimension n+p. Let A be the second fundamental form of the immersion, and r the extrinsic distance from the origin. Suppose M has one end and inft supr(x)>t r2(x) |A|2(x) < C(n,p), then M is an affine n-plane, where C(n,p) are constants given by C(n,1) = n – 1 and C(n,p) = (2/3)(n – 1) when p > 1. 相似文献
14.
§1.IntroductionLetMbeann-dimensionalclosedminimalyimmersedsubmanifoldintheunitsphereSn+p,Sthesequreofthelengthofthesecondfund... 相似文献
15.
单位球面的三维紧致极小子流形 总被引:3,自引:0,他引:3
本文得到高维球面上三维紧致极小子流形的若干刚性定理.在一个整体拚挤条件下,数量曲率的拚挤常数被改进了,也对李奇曲率的拚挤问题进行了讨论. 相似文献
16.
设N n+p是截面曲率KN 满足1/2 <δ≤ KN≤ 1 的n+p维局部对称完备的δ-Pinching黎曼流形. Mn是Nn+p 的紧致极小子流形. 该文讨论了这类子流形关于Ricci曲率有关的Pinching定理. 相似文献
17.
Let M be a concircularly flat totally real minimal submanifold in CP~4. The infimum V_m of the volume V(M) of M is obtained, also the necessary and sufficient conditions of "V(M)=V_m" is given. 相似文献
18.
51.IntroductionAquaternionKaehlermanifoldisdefinedasa4m-dimensionalRiemannianmanifoldwhoseholonomygroupiscontainedinSp(m).Sp(1)withtheadditionalconditionform=lthatitisaself-dualEinsteinspace.AquaternionprojectivespaceQP:)isaquaternionKeahlermanifoldwithconstantquaternionsectionalcurvaturec>O.AcomplexprojectivespaceCP2)withconstantholomorphicsectionalcurvatureccanbeisometricallyimbeddedinQP:)asatthtallygeodesicsubmanifold.LetMbeannsidimensionalRiemannianmanifoldander:M-Qer).-.'an1sometr1… 相似文献
19.
ARemarkonHarmonicMapsBetweenPseudo-RiemannianSpheresDingQing(丁青)(InstituteofMathematics,FudanUniversity,Shaghai,200433)WangJi... 相似文献
20.
Let M be a concircularly fiat totally real minimal submanifold in CP4. The infimum Vm of the volume V (M) of M is obtained, also the necessary and sufficient conditions of "V(M)=Vm" is given. 相似文献