共查询到19条相似文献,搜索用时 138 毫秒
1.
Liang Zhang 《高校应用数学学报(英文版)》2008,23(2):227-232
This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved. 相似文献
2.
A class of twisted special Lagrangian submanifolds in T~*R~n and a kind of austere submanifold from conormal bundle of minimal surface of R~3 are constructed. 相似文献
3.
Ying-bo Han 《高校应用数学学报(英文版)》2008,23(1):65-68
A class of twisted special Lagrangian submanifolds in T*R^n and a kind of austere submanifold from conormal bundle of minimal surface of R^3 are constructed. 相似文献
4.
CHEN Jing & BAI Yuzhen Department of Mathematics Nanjing University Nanjing China Department of Mathematics Qufu Normal University Qufu China 《中国科学A辑(英文版)》2006,49(12):1864-1866
Mane conjectured that every minimal measure in the generic Lagrangian systems is uniquely ergodic. In this paper, we will show that the answer to the Mane's conjecture is negative by analyzing the structure of the supports of minimal probability measures for some kinds of the Lagrangian systems. 相似文献
5.
DONG Yuxin & LU Guozhen Institute of Mathematics Fudan University Shanghai China Department of Mathematics Wayne State University Detroit MI 《中国科学A辑(英文版)》2005,48(11):1505-1516
In this paper, we determine all second order minimal Lagrangian submanifolds in complex space forms whose cubic forms have the largest non-trivial continuous symmetries. We describe these minimal Lagrangian submanifolds from the viewpoint of Bryant and study their geometric properties. 相似文献
6.
Xingxiao LI 《数学年刊B辑(英文版)》2022,43(3):473-482
In this paper, the authors give a characterization theorem for the standard tori S1(a) × S1(b), a, b > 0, as the compact Lagrangian ξ-submanifolds in the two-dimensional complex Euclidean space C2 , and obtain the best version of a former rigidity theorem for compact Lagrangian ξ-submanifold in C2 . Furthermore, their argument in this paper also proves a new rigidity theorem which is a direct generalization of a rigidity theorem by Li and Wang for Lagrangian self-shrinkers in C2. 相似文献
7.
Robert L. BRYANT 《数学年刊B辑(英文版)》2006,27(1)
Let SO(n) act in the standard way on Cn and extend this action in the usual way to Cn 1 =C Cn. It is shown that a nonsingular special Lagrangian submanifold L (?) Cn 1 that is invariant under this SO(n)-action intersects the fixed C (?) Cn 1 in a nonsingular real-analytic arc A (which may be empty). If n > 2, then A has no compact component. Conversely, an embedded, noncompact nonsingular real-analytic arc A(?)C lies in an embedded nonsingular special Lagrangian submanifold that is SO(n)-invariant. The same existence result holds for compact A if n = 2. If A is connected, there exist n distinct nonsingular SO(n)-invariant special Lagrangian extensions of A such that any embedded nonsingular SO(n)-invariant special Lagrangian extension of A agrees with one of these n extensions in some open neighborhood of A. The method employed is an analysis of a singular nonlinear pde and ultimately calls on the work of Gerard and Tahara to prove the existence of the extension. 相似文献
8.
Tong Zhu LI 《数学学报(英文版)》2005,21(6):1525-1534
Let f : M → R3 be an oriented surface with non-degenerate second fundamental form. We denote by H and K its mean curvature and Gauss curvature. Then the Laguerre volume of f, defined by L(f) = f(H2 - K)/KdM, is an invariant under the Laguerre transformations. The critical surfaces of the functional L are called Laguerre minimal surfaces. In this paper we study the Laguerre minimal surfaces in R^3 by using the Laguerre Gauss map. It is known that a generic Laguerre minimal surface has a dual Laguerre minimal surface with the same Gauss map. In this paper we show that any surface which is not Laguerre minimal is uniquely determined by its Laguerre Gauss map. We show also that round spheres are the only compact Laguerre minimal surfaces in R^3. And we give a classification theorem of surfaces in R^3 with vanishing Laguerre form. 相似文献
9.
LI Qiuyue & REN Yanxia LMAM School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2005,48(12):1683-1695
This paper gives probabilistic expressions of the minimal and maximal positive solutions of the partial differential equation -1/2△v(x) γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its complement Dc is compact, γ(x) is a positive bounded integrable function in D, and 1 < α≤ 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented. 相似文献
10.
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
11.
12.
该文证明了复射影空间中两种类型的法丛平坦全实伪脐子流形必是极小的,并在紧致的情形确定了它们的具体形状.此外,还说明了复射影空间中的全实全脐子流形一定不是法丛平坦的. 相似文献
13.
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
14.
本文给出了四元数射影空间中紧致全实伪脐子流形关于截面曲率和Ricci曲率的Pinching定理,并推广和改进了四元数射影空间中紧致全实极小流形的一些结果. 相似文献
15.
本文对于局部对称黎曼流形中的伪脐点子流形给出了一个积分不等式,推广了Chen,B.Y.的一个相应的结果. 相似文献
16.
复射影空间中的完备全实伪脐子流形 总被引:2,自引:0,他引:2
Let Mn be a totally real pseudo-umbilical submanifold in a complex projective space CPn+p. In this paper, we study the position of completeness of Mn. By choosing a suitable frame field, we obtain a rigidity theorem such that Mn becomes totally umbilical submanifold and improve the related results. 相似文献
17.
Yat-Ming Chan 《Annals of Global Analysis and Geometry》2009,35(1):91-114
In this paper we extend our previous results on resolving conically singular Calabi–Yau 3-folds (Chan, Quart. J. Math. 57:151–181,
2006; Quart. J. Math., to appear) to include the desingularizations of special Lagrangian (SL) 3-folds with conical singularities
that occur at the same points of the ambient Calabi–Yau. The gluing construction of the SL 3-folds is achieved by applying
Joyce’s analytic result (Joyce, Ann. Global. Anal. Geom. 26: 1–58, 2004, Thm. 5.3) on deforming Lagrangian submanifolds to
nearby special Lagrangian submanifolds. Our result will in principle be able to construct more examples of compact SL submanifolds
in compact Calabi–Yau manifolds. Various explicit examples and applications illustrating the result in this paper can be found
in the sequel (Chan, Ann. Global. Anal. Geom., to appear). 相似文献
18.
关于复射影空间中的全实伪脐子流形 总被引:2,自引:1,他引:1
设$M^n$是复射影空间${\bf C}P^{n+p}$中的全实子流形. 本文研究$M^n$的平行脐性法向量场在法丛中的位置. 在$p>0$的情形通过选取合适的标架场, 得到具有平行平均曲率向量的全实伪脐子流形关于第二基本形式模长平方的一个Pinching定理. 相似文献
19.
Roberto Paoletti 《Proceedings of the American Mathematical Society》2008,136(11):4011-4017
This paper deals with the asymptotic expansions describing the quantum states associated to Bohr Sommerfeld Lagrangian submanifolds of a compact Kähler manifold, in the context of geometric quantization. More precisely, it provides an improvement on a result of the work of Debernardi and the author (2006), describing a natural factorization of the expansion and providing certain remainder estimates.