共查询到20条相似文献,搜索用时 15 毫秒
1.
Bang-Yen Chen 《Monatshefte für Mathematik》1980,90(3):185-194
A surfaceM in a Riemannian manifold is said to have parallel normalized mean curvature vector if the mean curvature vector is nonzero and the unit vector in the direction of the mean curvature vector is parallel in the normal bundle. In this paper, it is proved that every analytic surface in a euclideanm-spaceE
m
with parallel normalized mean curvature vector must either lies in aE
4 or lies in a hypersphere ofE
m
as a minimal surface. Moreover, it is proved that if a Riemann sphere inE
m
has parallel normalized mean curvature vector, then it lies either in aE
3 or in a hypersphere ofE
m
as a minimal surfaces. Applications to the classification of surfaces with constant Gauss curvature and with parallel normalized mean curvature vector are also given. 相似文献
2.
Sheng Zhi Zhu 《数学学报(英文版)》2010,26(8):1449-1456
We prove that the set of vector fields satisfying the C1 stable shadowable property on closed surfaces is characterized as the set of Morse-Smale vector fields. Hence, the vector fields satisfying shadowing property on closed surfaces are C1 dense. 相似文献
3.
Domenico Perrone 《Mathematische Zeitschrift》2009,263(1):125-147
It is well known that a Hopf vector field on the unit sphere S
2n+1 is the Reeb vector field of a natural Sasakian structure on S
2n+1. A contact metric manifold whose Reeb vector field ξ is a harmonic vector field is called an H-contact manifold. Sasakian and K-contact manifolds, generalized (k, μ)-spaces and contact metric three-manifolds with ξ strongly normal, are H-contact manifolds. In this paper we study, in dimension three, the stability with respect to the energy of the Reeb vector
field ξ for such special classes of H-contact manifolds (and with respect to the volume when ξ is also minimal) in terms of Webster scalar curvature. Finally, we extend for the Reeb vector field of a compact K-contact (2n+1)-manifold the obtained results for the Hopf vector fields to minimize the energy functional with mean curvature correction.
Supported by funds of the University of Lecce and M.I.U.R.(PRIN). 相似文献
4.
Bang‐Yen Chen 《Mathematische Nachrichten》2005,278(11):1242-1281
A Lagrangian submanifold is called Maslovian if its mean curvature vector H is nowhere zero and its Maslov vector field JH is a principal direction of AH . In this article we classify Maslovian Lagrangian surfaces of constant curvature in complex projective plane CP 2 as well as in complex hyperbolic plane CH 2. We prove that there exist 14 families of Maslovian Lagrangian surfaces of constant curvature in CP 2 and 41 families in CH 2. All of the Lagrangian surfaces of constant curvature obtained from these families admit a unit length Killing vector field whose integral curves are geodesics of the Lagrangian surfaces. Conversely, locally (in a neighborhood of each point belonging to an open dense subset) every Maslovian Lagrangian surface of constant curvature in CP 2 or in CH 2 is a surface obtained from these 55 families. As an immediate by‐product, we provide new methods to construct explicitly many new examples of Lagrangian surfaces of constant curvature in complex projective and complex hyperbolic planes which admit a unit length Killing vector field. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A ,φ in the Lorenz gauge, we establish boundary conditions on the potentials themselves rather than on the field quantities. This permits the development of a well‐conditioned second‐kind Fredholm integral equation that has no spurious resonances, avoids low‐frequency breakdown, and is insensitive to the genus of the scatterer. The equations for the vector and scalar potentials are decoupled. That is, the unknown scalar potential defining the scattered field, φscat, is determined entirely by the incident scalar potential φinc. Likewise, the unknown vector potential defining the scattered field, A scat is determined entirely by the incident vector potential Ainc. This decoupled formulation is valid not only in the static limit but for arbitrary ω ≥ 0$. © 2016 Wiley Periodicals, Inc. 相似文献
6.
SHARIEF DESHMUKH 《Proceedings Mathematical Sciences》2011,121(2):171-179
In this paper, we classify real hypersurfaces in the complex projective space
C P\fracn+12C P^{\frac{n+1}{2}} whose structure vector field is a φ-analytic vector field (a notion similar to analytic vector fields on complex manifolds). We also define Jacobi-type vector
fields on a Riemannian manifold and classify real hypersurfaces whose structure vector field is a Jacobi-type vector field. 相似文献
7.
In this paper it is shown that the structurally stable polynomial vector fields on the torusT
2, with singularities, are open and dense in the set of such vector fields. Many kinds of distinct dynamical phenomena are
also presented by a list of examples including the Cherry flows. The above result works for analytical vector fields onT
2 with the same proof. 相似文献
8.
Let E
0
be a holomorphic vector bundle over P1(C) and †0
be a meromorphic connection of E
0. We introduce the notion of an integrable connection that describes the movement of the poles of †0
in the complex plane with integrability preserved. We show the that such a deformation exists under sufficiently weak conditions
on the deformation space. We also show that if the vector bundle E0 is trivial, then the solutions of the corresponding nonlinear equations extend meromorphically to the deformation space. 相似文献
9.
It is known that a vector bundle E on a smooth projective curve Y defined over an algebraically closed field is semistable if and only if there is a vector bundle F on Y such that both H0(X,EF) and H1(X,EF) vanishes. We extend this criterion for semistability to vector bundles on curves defined over perfect fields. Let X be a geometrically irreducible smooth projective curve defined over a perfect field k, and let E be a vector bundle on X. We prove that E is semistable if and only if there is a vector bundle F on X such that Hi(X,EF)=0 for all i. We also give an explicit bound for the rank of F. 相似文献
10.
Abstract: In this paper we prove that a hypoelliptic vector fields on the torus Tn may be transformed by a smooth diffeomorphism of torus Tn into a vector field with constant coefficients, which moreover satisfy a Diophantine condition. We also discuss the relation between the hypoelliptic vecttor fields and the almost periodic motions on the torus Tn 相似文献
11.
Francesco Bottacin 《Mathematische Nachrichten》2000,220(1):33-44
In this paper we prove that the moduli spaces of framed vector bundles over a surface X, satisfying certain conditions, admit a family of Poisson structures parametrized by the global sections of a certain line bundle on X. This generalizes to the case of framed vector bundles previous results obtained in [B2] for the moduli space of vector bundles over a Poisson surface. As a corollary of this result we prove that the moduli spaces of framed SU(r) – instantons on S4 = ℝ4 ∪ {∞} admit a natural holomorphic symplectic structure. 相似文献
12.
Giulio Cotignoli 《代数通讯》2013,41(7):2564-2573
In the mid 1970s, Hartshorne conjectured that, for all n > 7, any rank 2 vector bundles on ? n is a direct sum of line bundles. This conjecture remains still open. In this paper, we construct indecomposable rank two vector bundles on a large class of Fano toric varieties. Unfortunately, this class does not contain ? n . 相似文献
13.
The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form ∫01 W dW, where W(r) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA processes, the theory involves weak convergence to matrix stochastic integrals of the form ∫01 B dB′, where B(r) is vector Brownian motion with a non-scalar covariance matrix. This paper studies the weak convergence of sample covariance matrices to ∫01 B dB′ under quite general conditions. The theory is applied to vector autoregressions with integrated processes. 相似文献
14.
Let T be an order bounded disjointness preserving operator on an Archimedean vector lattice. The main result in this paper shows
that T is algebraic if and only if there exist natural numbers m and n such that n ≥ m, and Tn!, when restricted to the vector sublattice generated by the range of Tm, is an algebraic orthomorphism. Moreover, n (respectively, m) can be chosen as the degree (respectively, the multiplicity of 0 as a root) of the minimal polynomial of T. In the process of proving this result, we define strongly diagonal operators and study algebraic order bounded disjointness
preserving operators and locally algebraic orthomorphisms. In addition, we introduce a type of completeness on Archimedean
vector lattices that is necessary and sufficient for locally algebraic orthomorphisms to coincide with algebraic orthomorphisms. 相似文献
15.
《Quaestiones Mathematicae》2013,36(3):291-303
Abstract Most homotopies considered in the literature are linear homotopies of the form h i (λ) = λx i + (1—λ)y i , 0 ≤ λ ≤ 1. Although these prove to be adequate in most instances, they lack direct geometric significance because {h i (λ) | 0 ≤ λ ≤ 1} are not orbits of a vector field. On the other hand, the nonlinear homotopy g i (s) = e s x i + (1—e s )y i ,—∞ ≤ s ≤ 0, are orbits of a vector field (i.e., dg i /ds = g i —y i , g i (0) = x i ), and thus have direct geometric significance. This suggests that useful results can be obtained by replacing linear homotopy by transport along flows of smooth vector fields. The purpose of this paper is to elaborate on this simple idea. We define prehomotopy operators induced by vector fields on a manifold. These allow us to obtain finite transport relations and pre-Poincaré lemmas that generalize the classical results. They are shown to reproduce the classical results as asymptotic limits and to obtain representations of all solutions of complete systems of exterior differential equations on a star shaped region of a manifold. 相似文献
16.
R. Abreu‐Blaya J. Bory‐Reyes M. Shapiro 《Mathematical Methods in the Applied Sciences》2006,29(15):1861-1881
Given a domain Ω in ?3 with rectifiable boundary, we consider main integral, and some other, theorems for the theory of Laplacian (sometimes called solenoidal and irrotational, or harmonic) vector fields paying a special attention to the problem of decomposing a continuous vector field, with an additional condition, u on the boundary Γof Ω ? ?3 into a sum u = u++u? were u± are boundary values of vector fields which are Laplacian in Ω and its complement respectively. Our proofs are based on the intimate relations between Laplacian vector fields theory and quaternionic analysis for the Moisil–Theodorescu operator. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
17.
Marte Rørvik Høyem 《Acta Appl Math》2010,109(1):61-73
We consider the Lie algebra that corresponds to the Lie pseudogroup of all conformal transformations on the plane. This conformal
Lie algebra is canonically represented as the Lie algebra of holomorphic vector fields in ℝ2≃ℂ. We describe all representations of
\mathfrakg\mathfrak{g}
via vector fields in J
0ℝ2=ℝ3(x,y,u), which project to the canonical representation, and find their algebra of scalar differential invariants. 相似文献
18.
LeM be a (2m+2)-dimensional Riemannian manifold with two structure vector fieldsξ
r
(r=2m+1, 2m+2) and letη
r
=ξ
r
b
be their corresponding covectors (or Pfaffians). These vector fields define onM a 2-almost contact structure.
If the 2-formϕ=η
2m+1∧η
2m+2 is harmonic, then, following S. Tachibana [12],M is a Tachibana manifold and in this caseM is covered with 2 families of minimal submanifolds tangent toD
⊥={ξ
r} and its complementary orthogonal distributionD
⊤.
On such a manifold a canonical eigenfunction α of the Laplacian is associated. Since the corresponding eingenvalue is negative,M cannot be compact. Any horizontal vector fieldX orthogonal to α# is a skew-symmetric Killing vector field (see [6]).
Next, we assume that the Tachibana manifoldM under consideration is endowed with a framedf-structure defined by an endomorphism ϕ of the tangent bundleTM. Infinitesimal automorphisms of the symplectic form Ω
ϕ
are obtained. 相似文献
19.
Antonios Charalambopoulos Kiriakie Kiriaki 《Mathematical Methods in the Applied Sciences》1992,15(8):547-558
In this paper a necessary and sufficient condition for a pair of vector functions to be radiation patterns is presented. More precisely, it is proved that two vector functions, the first in the radial direction and the second in the tangential one, are radiation patterns if and only if there are two entire harmonic vector functions whose radial and tangential projections, respectively, are identical with the previous functions on the unit sphere and whose L2-norm over a sphere of radius R is a function of exponential type in the variable R. 相似文献
20.
Uğur Dursun 《Journal of Geometry》2007,86(1-2):73-80
Let M be a 3-dimensional submanifold of the Euclidean space E5 such that M is not of 1-type. We show that if M is flat and of null 2-type with constant mean curvature and non-parallel mean curvature vector then the normal bundle is
flat. We also prove that M is an open portion of a 3-dimensional helical cylinder if and only if M is flat and of null 2-type with constant mean curvature and non-parallel mean curvature vector. 相似文献