共查询到20条相似文献,搜索用时 46 毫秒
1.
Motivated by the theory of isoparametric hypersurfaces,we study submanifolds whose tubular hypersurfaces have some constant higher order mean curvatures.Here a k-th order mean curvature Q_k~v(k ≥ 1) of a submanifold M~n-is defined as the k-th power sum of the principal curvatures,or equivalently,of the shape operator with respect to the unit normal vector v.We show that if all nearby tubular hypersurfaces of M have some constant higher order mean curvatures,then the submanifold M itself has some constant higher order mean curvatures Q_k~v independent of the choice of v.Many identities involving higher order mean curvatures and Jacobi operators on such submanifolds are also obtained.In particular,we generalize several classical results in isoparametric theory given by E.Cartan,K.Nomizu,H.F.Miinzner,Q.M.Wang,et al.As an application,we finally get a geometrical filtration for the focal submanifolds of isoparametric functions on a complete Riemannian manifold. 相似文献
2.
Jerzy Jezierski 《中国科学 数学(英文版)》2017,60(9):1579-1590
There are two algebraic lower bounds of the number of n-periodic points of a self-map f : M → M of a compact smooth manifold of dimension at least 3: NF_n(f) = min{#Fix(g~n); g ~ f; g continuous} and NJD_n(f) = min{#Fix(g~n); g ~ f; g smooth}. In general, NJD_n(f) may be much greater than NF_n(f). We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism,the equality NF_n(f) = NJD_n(f) holds for all n ? all eigenvalues of a quotient cohomology homomorphism induced by f have moduli 1. 相似文献
3.
Hong Zhang 《manuscripta mathematica》2016,149(1-2):153-170
Let (M, g 0) be a compact Riemann surface with boundary and with negative Euler characteristic. Let f(x) be a strictly negative smooth function on \({\bar{M}}\) and denote by \({\sigma(x)}\) the value of f in the interior and \({\zeta(x)}\) the value of f on the boundary. By studying the evolution of curvatures on M, we prove that there exist a constant \({\lambda_\infty}\) and a conformal metric \({g_\infty}\) such that \({\lambda_\infty\sigma(x)}\) and \({\lambda_\infty\zeta(x)}\) can be realized as the Gaussian curvature and boundary geodesic curvature of \({g_\infty}\) respectively. 相似文献
4.
Parametric polynomial surface is a fundamental element in CAD systems. Since the most of the classic minimal surfaces are represented by non-parametric polynomial, it is interesting to study the minimal surfaces represented in parametric polynomial form. Recently,Ganchev presented the canonical principal parameters for minimal surfaces. The normal curvature of a minimal surface expressed in these parameters determines completely the surface up to a position in the space. Based on this result, in this paper, we study the bi-quintic isothermal minimal surfaces. According to the condition that any minimal isothermal surface is harmonic,we can acquire the relationship of some control points must satisfy. Follow up, we obtain two holomorphic functions f(z) and g(z) which give the Weierstrass representation of the minimal surface. Under the constrains that the minimal surface is bi-quintic, f(z) and g(z) can be divided into two cases. One case is that f(z) is a constant and g(z) is a quadratic polynomial, and another case is that the degree of f(z) and g(z) are 2 and 1 respectively. For these two cases,we transfer the isothermal parameter to canonical principal parameter, and then compute their normal curvatures and analyze the properties of the corresponding minimal surfaces. Moreover,we study some geometric properties of the bi-quintic harmonic surfaces based on the B′ezier representation. Finally, some numerical examples are demonstrated to verify our results. 相似文献
5.
We give all solutions of the equation f(n) = g(n) + h(n) for every n ∈ ?, where f is a completely multiplicative, g is a 2-additive, and h is a 3-additive function. We also determine all completely multiplicative functions f and all q-additive functions g for which f(n) = g 2(n) for every n ∈ ?. 相似文献
6.
A. V. Pukhlikov 《Proceedings of the Steklov Institute of Mathematics》2012,276(1):234-249
We obtain upper bounds for the multiplicity of an isolated solution of a system of equations f 1 = ... = f M = 0 in M variables, where the set of polynomials (f 1, ..., f M ) is a tuple of general position in a subvariety of a given codimension which does not exceed M, in the space of tuples of polynomials. It is proved that as M → ∞ this multiplicity grows no faster than \(\sqrt M \exp \left[ {\omega \sqrt M } \right]\), where ω > 0 is a certain constant. 相似文献
7.
Let G be a graph, and g, f: V (G) → Z+ with g(x) ≤ f(x) for each x ∈ V (G). We say that G admits all fractional (g, f)-factors if G contains an fractional r-factor for every r: V (G) → Z+ with g(x) ≤ r(x) ≤ f(x) for any x ∈ V (G). Let H be a subgraph of G. We say that G has all fractional (g, f)-factors excluding H if for every r: V (G) → Z+ with g(x) ≤ r(x) ≤ f(x) for all x ∈ V (G), G has a fractional r-factor F h such that E(H) ∩ E(F h ) = θ, where h: E(G) → [0, 1] is a function. In this paper, we show a characterization for the existence of all fractional (g, f)-factors excluding H and obtain two sufficient conditions for a graph to have all fractional (g, f)-factors excluding H. 相似文献
8.
P. Niu Y. Xu 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2016,51(3):160-165
The paper is devoted to the normal families of meromorphic functions and shared functions. Generalizing a result of Chang (2013), we prove the following theorem. Let h (≠≡ 0,∞) be a meromorphic function on a domain D and let k be a positive integer. Let F be a family of meromorphic functions on D, all of whose zeros have multiplicity at least k + 2, such that for each pair of functions f and g from F, f and g share the value 0, and f(k) and g(k) share the function h. If for every f ∈ F, at each common zero of f and h the multiplicities mf for f and mh for h satisfy mf ≥ mh + k + 1 for k > 1 and mf ≥ 2mh + 3 for k = 1, and at each common pole of f and h, the multiplicities nf for f and nh for h satisfy nf ≥ nh + 1, then the family F is normal on D. 相似文献
9.
Let f: M → M be a partially hyperbolic diffeomorphism on a closed Riemannian manifold with uniformly compact center foliation. We show that if the center foliation of f is of dimension one then the topological entropy is constant on a small C1 neighborhood of f. 相似文献
10.
Rajeeva L. Karandikar 《印度理论与应用数学杂志》2017,48(4):469-493
In Karandikar-Rao [11], the quadratic variation [M, M] of a (local) martingale was obtained directly using only Doob’s maximal inequality and it was remarked that the stochastic integral can be defined using [M, M], avoiding using the predictable quadratic variation 〈M, M〉 (of a locally square integrable martingale) as is usually done. This is accomplished here- starting with the result proved in [11], we construct ∫ f dX where X is a semimartingale and f is predictable and prove dominated convergence theorem (DCT) for the stochastic integral. Indeed, we characterize the class of integrands f for this integral as the class L(X) of predictable processes f such that |f| serves as the dominating function in the DCT for the stochastic integral. This observation seems to be new.We then discuss the vector stochastic integral ∫ 〈f, dY〉 where f is ? d valued predictable process, Y is ? d valued semimartingale. This was defined by Jacod [6] starting from vector valued simple functions. Memin [13] proved that for (local) martingales M1, … M d : If N n are martingales such that N t n → N t for every t and if ?f n such that N t n = ∫ 〈f n , dM〉, then ?f such that N = ∫ 〈f, dM〉.Taking a cue from our characterization of L(X), we define the vector integral in terms of the scalar integral and then give a direct proof of the result due to Memin stated above.This completeness result is an important step in the proof of the Jacod-Yor [4] result on martingale representation property and uniqueness of equivalent martingale measure. This result is also known as the second fundamental theorem of asset pricing. 相似文献
11.
A. A. Illarionov 《Proceedings of the Steklov Institute of Mathematics》2017,299(1):96-108
Functional equations of the form f(x + y)g(x ? y) = Σ j=1 n α j (x)β j (y) as well as of the form f1(x + z)f2(y + z)f3(x + y ? z) = Σ j=1 m φ j (x, y)ψ j (z) are solved for unknown entire functions f, g,α j , β j : ? → ? and f1, f2, f3, ψ j : ? → ?, φ j : ?2 → ? in the cases of n = 3 and m = 4. 相似文献
12.
Manseob Lee 《数学学报(英文版)》2016,32(8):975-981
Let f:M~d→M~d(d≥2) be a diffeomorphism on a compact C~∞ manifold on M.If a diffeomorphism f belongs to the C~1-interior of the set of all diffeomorphisms having the barycenter property,then f is Ω-stable.Moreover,if a generic diffeomorphism f has the barycenter property,then f is Ω-stable.We also apply our results to volume preserving diffeomorphisms. 相似文献
13.
We investigate the equiconvergence on TN = [?π, π)N of expansions in multiple trigonometric Fourier series and in the Fourier integrals of functions f ∈ Lp(TN) and g ∈ Lp(RN), p > 1, N ≥ 3, g(x) = f(x) on TN, in the case where the “partial sums” of these expansions, i.e., Sn(x; f) and Jα(x; g), respectively, have “numbers” n ∈ ZN and α ∈ RN (nj = [αj], j = 1,..., N, [t] is the integral part of t ∈ R1) containing N ? 1 components which are elements of “lacunary sequences.” 相似文献
14.
In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM~k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M~j(s), M~k(t)) for s, t ≤ n, M~j, M~k are g-twisted V modules, if V is g-rational. 相似文献
15.
Let (M n , g)(n ≥ 3) be an n-dimensional complete Riemannian manifold with harmonic curvature and positive Yamabe constant. Denote by R and R m? the scalar curvature and the trace-free Riemannian curvature tensor of M, respectively. The main result of this paper states that R m? goes to zero uniformly at infinity if for \(p\geq \frac n2\), the L p -norm of R m? is finite. Moreover, If R is positive, then (M n , g) is compact. As applications, we prove that (M n , g) is isometric to a spherical space form if for \(p\geq \frac n2\), R is positive and the L p -norm of R m? is pinched in [0, C 1), where C 1 is an explicit positive constant depending only on n, p, R and the Yamabe constant. We give an isolation theorem of the trace-free Ricci curvature tensor of compact locally conformally flat Riemannian n-manifolds with constant positive scalar curvature, which extends Theorem 1 of Hebey and M. Vaugon (J. Geom. Anal. 6, 531–553, 1996). This result is sharp, and we can precisely characterize the case of equality. In particular, when n = 4, we recover results by Gursky (Indiana Univ. Math. J. 43, 747–774, 1994; Ann. Math. 148, 315–337, 1998). 相似文献
16.
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
17.
This paper introduces the notion of robust hyperbolicity along periodic orbits homoclinically related to p (RNUHP) for conservative diffeomorphisms. It is proved that if f ∈ Diff1+ m (M) is RNUHP, then f is Anosov. It is also shown that f admits a dominated splitting, provided that f is expansive conservative stable. 相似文献
18.
H. A. Atia 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2016,51(5):222-226
In this paper we obtain sufficient conditions for the bi-harmonic differential operator A = ΔE2 + q to be separated in the space L2 (M) on a complete Riemannian manifold (M,g) with metric g, where ΔE is the magnetic Laplacian onM and q ≥ 0 is a locally square integrable function on M. Recall that, in the terminology of Everitt and Giertz, the differential operator A is said to be separated in L2 (M) if for all u ∈ L2 (M) such that Au ∈ L2 (M) we have ΔE2u ∈ L2 (M) and qu ∈ L2 (M). 相似文献
19.
E. E. Ditkovskaya 《Russian Mathematics (Iz VUZ)》2010,54(7):49-55
We show that the identities R 1, R 2 and R 3 for an almost Hermitian structure S on the base of the canonical principal T 1-bundle are equivalent to their contact analogs for the induced almost contact metric structure S # on the total space of this bundle. We prove that the canonical connection of the canonical principal T 1-bundle over a Hermitian or a quasi-Kähler manifold of class R 3 is normal. We also prove that that the canonical connection of the canonical principal T 1-bundle over a Vaisman-Gray manifold M of class R 3 is normal if and only if the Lee vector of M belongs to the center of the adjoint K-algebra. 相似文献
20.
Given a prime p, we consider the dynamical system generated by repeated exponentiations modulo p, that is, by the map \({u \mapsto f_g(u)}\), where f g (u) ≡ g u (mod p) and 0 ≤ f g (u) ≤ p ? 1. This map is in particular used in a number of constructions of cryptographically secure pseudorandom generators. We obtain nontrivial upper bounds on the number of fixed points and short cycles in the above dynamical system. 相似文献