共查询到20条相似文献,搜索用时 714 毫秒
1.
We give a procedure to ‘average’ canonically C1-close Legendrian submanifolds of contact manifolds. As a corollary we obtain that, whenever a compact group action leaves
a Legendrian submanifold almost invariant, there is an invariant Legendrian submanifold nearby.
Mathematics Subject Classification (2000): 53D10. 相似文献
2.
In this paper we show how to embed a time slice of the Schwarzchild spacetime that models the outer space around a massive star, as a Lagrangian submanifold invariant under the standard action of the special orthogonal group on complex Euclidean space. This result is generalized for rotationally invariant metrics that can be considered as higher-dimensional versions of Schwarzchild's and these submanifolds are locally characterized as the only ones with zero scalar curvature inside the above family. 相似文献
3.
Summary We define a notion of contact totally umbilical submanifolds of Sasakian space forms corresponds to those of totally umbilical
submanifolds of complex space forms. We study a contact totally umbilical submanifold M of a Sasakian space form
(c ≠ −3) and prove that M is an invariant submanifold or an anti-invariant submanifold. Furthermore we study a submanifold
M with parallel second fundamental form of a Sasakian space form
(c ≠ 1) and prove that M is invariant or anti-invariant.
Entrata in Redazione il 7 settembre 1976. 相似文献
4.
O. I. Mokhov 《Functional Analysis and Its Applications》2006,40(1):11-23
We solve the problem of describing all nonlocal Hamiltonian operators of hydrodynamic type with flat metrics. This problem is equivalent to describing all flat submanifolds with flat normal bundle in a pseudo-Euclidean space. We prove that every such Hamiltonian operator (or the corresponding submanifold) specifies a pencil of compatible Poisson brackets, generates bihamiltonian integrable hierarchies of hydrodynamic type, and also defines a family of integrals in involution. We prove that there is a natural special class of such Hamiltonian operators (submanifolds) exactly described by the associativity equations of two-dimensional topological quantum field theory (the Witten-Dijkgraaf-Verlinde-Verlinde and Dubrovin equations). We show that each N-dimensional Frobenius manifold can locally be represented by a special flat N-dimensional submanifold with flat normal bundle in a 2N-dimensional pseudo-Euclidean space. This submanifold is uniquely determined up to motions. 相似文献
5.
In this paper, we have studied submanifolds especially, totally umbilical submanifolds of generalized \((k,\mu )\)-space-forms. We have found a necessary and sufficient condition for such submanifolds to be either invariant or anti-invariant. It is also shown that every totally umbilical submanifold of a generalized \((k,\mu )\)-space-form is a pseudo quasi-Einstein manifold. 相似文献
6.
Heiko Ewert 《Proceedings of the American Mathematical Society》1998,126(8):2443-2452
A submanifold in a symmetric space is called equifocal if it has a globally flat abelian normal bundle and its focal data is invariant under normal parallel transportation. This is a generalization of the notion of isoparametric submanifolds in Euclidean spaces. To each equifocal submanifold, we can associate a Coxeter group, which is determined by the focal data at one point. In this paper we prove that an equifocal submanifold in a simply connected compact symmetric space is a non-trivial product of two such submanifolds if and only if its associated Coxeter group is decomposable. As a consequence, we get a similar splitting result for hyperpolar group actions on compact symmetric spaces. These results are an application of a splitting theorem for isoparametric submanifolds in Hilbert spaces by Heintze and Liu.
7.
A sphere of dimension 4n+3 admits three Sasakian structures and it is natural to ask if a submanifold can be an integral submanifold for more than one of the contact structures. In the 7-sphere it is possible to have curves which are Legendre curves for all three contact structures and there are 2 and 3-dimensional submanifolds which are integral submanifolds of two of the contact structures. One of the results here is that if a 3-dimensional submanifold is an integral submanifold of one of the Sasakian structures and invariant with respect to another, it is an integral submanifold of the remaining structure and is a principal circle bundle over a holmophic Legendre curve in complex projective 3-space. 相似文献
8.
O. I. Mokhov 《Theoretical and Mathematical Physics》2007,152(2):1183-1190
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions
of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of
flat torsionless potential submanifolds. We show that all flat torsionless potential submanifolds in pseudo-Euclidean spaces bear natural structures
of Frobenius algebras on their tangent spaces. These Frobenius structures are generated by the corresponding flat first fundamental
form and the set of the second fundamental forms of the submanifolds (in fact, the structural constants are given by the set
of the Weingarten operators of the submanifolds). We prove that each N-dimensional Frobenius manifold can be locally represented
as a flat torsionless potential submanifold in a 2N-dimensional pseudo-Euclidean space. By our construction, this submanifold
is uniquely determined up to motions. Moreover, we consider a nonlinear system that is a natural generalization of the associativity
equations, namely, the system describing all flat torsionless submanifolds in pseudo-Euclidean spaces, and prove that this
system is integrable by the inverse scattering method.
To the memory of my wonderful mother Maya Nikolayevna Mokhova (4 May 1926–12 September 2006)
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 368–376, August, 2007. 相似文献
9.
Yongbing Zhang 《数学研究》2021,54(2):200-226
It was proved by Graham and Witten in 1999 that conformal invariants of submanifolds can be obtained via volume renormalization of minimal surfaces in conformally compact Einstein manifolds. The conformal invariant of a submanifold $\Sigma$ is contained in the volume expansion of the minimal surface which is asymptotic to $\Sigma$ when the minimal surface approaches the conformaly infinity. In the paper we give the explicit expression of Graham-Witten's conformal invariant for closed four dimensional submanifolds and find critical points of the conformal invariant in the case of Euclidean ambient spaces. 相似文献
10.
XuSenlin ChenDongmei 《分析论及其应用》2004,20(4):383-390
The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized 相似文献
11.
12.
Sorin Dragomir 《Israel Journal of Mathematics》1988,61(2):199-210
The main results we obtain are as follows: an invariant submanifold of a Hopf manifold with semi-flat normal connection is
either a complex hypersurface or a totally-umbilical quasi-Einstein submanifold with a flat normal connection. The only totally-umbilical
invariant submanifolds of zero scalar curvature of a Hopf manifold are the totally-geodesic flat surfaces.
To Professor A. Cossu on the Occasion of his 65th Birthday 相似文献
13.
Damir Filipović 《Probability Theory and Related Fields》2000,118(3):323-341
Viability and invariance problems related to a stochastic equation in a Hilbert space H are studied. Finite dimensional invariant C
2 submanifolds of H are characterized. We derive Nagumo type conditions and prove a regularity result: any weak solution, which is viable in
a finite dimensional C
2 submanifold, is a strong solution.
These results are related to finding finite dimensional realizations for stochastic equations. There has recently been increased
interest in connection with a model for the stochastic evolution of forward rate curves.
Received: 15 April 1999 / Revised version: 4 February 2000 / Published online: 18 September 2000 相似文献
14.
On Invariant Submanifolds of C- and S-Manifolds 总被引:1,自引:0,他引:1
L. Di Terlizzi 《Acta Mathematica Hungarica》1999,85(3):229-239
We characterize totally geodesic invariant submanifolds of C- and S-manifolds. We prove that the second fundamental form is parallel if and only if the submanifold of an S-manifold is totally geodesic. We show that this is not true for the C-manifolds.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
关于局部对称空间中的伪脐子流形 总被引:8,自引:0,他引:8
本文讨论了局部对称完备黎曼流形中的紧致伪脐子流形,且具有平行平均山率向量场。得到了这类子流形成为全脐子流形及其余维数减小的几个拼挤定理。 相似文献
16.
In this paper, we study pseudo-slant submanifolds and their warped products in Kenmotsu manifolds. We obtain the necessary conditions that a pseudoslant submanifold is locally a warped product and establish an inequality for the squared norm of the second fundamental form in terms of the warping function. The equality case is also considered. 相似文献
17.
18.
Warped product manifolds are known to have applications in Physics. For instance, they provide an excellent setting to model
space-time near a black hole or a massive star (cf. [HONG, S. T.: Warped products and black holes, Nuovo Cimento Soc. Ital. Fis. B 120 (2005), 1227–1234]). The studies on warped product manifolds with extrinsic geometric point of view are intensified after
B. Y. Chen’s work on CR-warped product submanifolds of Kaehler manifolds. Later on, similar studies are carried out in the
setting of Sasakian manifolds by Hasegawa and Mihai. As Kenmotsu manifolds are themselves warped product spaces, it is interesting
to investigate warped product submanifolds of Kenmotsu manifolds. In the present note a larger class of warped product submanifolds
than the class of contact CR-warped product submanifolds is considered. More precisely the existence of warped product submanifolds
of a Kenmotsu manifold with one of the factors an invariant submanifold is ensured, an example of such submanifolds is provided
and a characterization for a contact CR-submanifold to be a contact CR-warped product submanifold is established. 相似文献
19.
Mukut Mani Tripathi Jeong-Sik Kim Seon-Bu Kim 《Proceedings Mathematical Sciences》2002,112(3):415-423
For submanifolds tangent to the structure vector field in locally conformal almost cosymplectic manifolds of pointwise constantφ-sectional curvature, we establish a basic inequality between the main intrinsic invariants of the submanifold on one side,
namely its sectional curvature and its scalar curvature; and its main extrinsic invariant on the other side, namely its squared
mean curvature. Some applications including inequalities between the intrinsic invariantδ
M
and the squared mean curvature are given. The equality cases are also discussed. 相似文献
20.
M. A. Beltagy 《Rendiconti del Circolo Matematico di Palermo》1985,34(2):219-225
Local convexity and convexity of submanifolds in a general Riemannian manifold have been defined. The propblem of isometric immersion of a submanifold into a unit sphere as a locally convex submanifold has been considered. The result we have arrived at is also true for the case of convex immersion. 相似文献