Lagrangian submanifolds in complex projective space CPn
Lagrangian submanifolds in complex projective space CPn
摘要
We first prove a basic theorem with respect to the moving frame along a Lagrangian immersion into the complex projective space CPn. Applying this theorem, we study the rigidity problem of Lagrangian submanifolds in CPn.
We first prove a basic theorem with respect to the moving frame along a Lagrangian immersion into the complex projective space CPn. Applying this theorem, we study the rigidity problem of Lagrangian submanifolds in CPn.
参考文献15
-
1Castro I, Li H Z, Urbano F. Hamiltonian-minimal Lagrangian submanifolds in complex space forms. Pacific J Math, 2006, 227(1): 43-63.
-
2Chen B Y, Dillen F, Verstraelen L, Vrancken L. An exotic totally real minimal immersion of S3 in CP3 and its characterisation. Proc Roy Soc Edinburgh Sect A, 1996, 126:153-165.
-
3chen Q, Xu S L. Rigidity of compact minimal submanifolds in a unit sphere. Geom Dedicata, 1993, 45:83-88.
-
4Chern S S, do Carmo M, Kobayashi S. Minimal submanifolds of a sphere with second fundamental form of constant length. In: Browder F E, ed. Functional Analysis and Related Fields. Berlin: Springer, 1970, 59-75.
-
5Ejiri N. Totally real minimal immersions of n-dimensional real space forms into n-dimensional complex space forms. Proc Amer Math Soc, 1982, 53:186-190.
-
6Ge J Q, Tang Z Z. A proof of the DDVV conjecture and its equality case. Pacific J Math, 2008, 273(1): 87-95.
-
7Griffiths P. On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence question in differential geometry. Duke Math J, 1974, 41: 775-814.
-
8Li A M, Li J M. An intrinsic rigidity theorem for minimal submanifolds in a sphere. Arch Math, 1992, 58:582-594.
-
9Li A M, Zhao G S. Totally real minimal submanifolds in CPn. Arch Math, 1994, 62: 562-568.
-
10Ma H. Hamiltonian stationary Lagrangian surfaces in CP2. Ann Global Anal Geom, 2005, 27:1-16.
-
1HU ZeJun,ZHANG YinShan.Isotropic Lagrangian submanifolds in the homogeneous nearly Khler S^3× S^3[J].Science China Mathematics,2017,60(4):671-684. 被引量：1
-
2Liang ZHANG,Weidong SONG,Songting YIN.On Pseudo-Umbilical Lagrangian Submanifolds in CP^3[J].Journal of Mathematical Research with Applications,2014,34(2):223-230.
-
3Henri ANCIAUX,Ildefonso CASTRO,Pascal ROMON.Lagrangian Submanifolds Foliated by(n-1)-spheres in R^(2n)[J].Acta Mathematica Sinica,English Series,2006,22(4):1197-1214.
-
4东瑜昕,韩英波.ON SPACELIKE AUSTERE SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACE[J].Acta Mathematica Scientia,2011,31(2):501-511.
-
5XIAQIAOLING,SHENYIBING.LOOP GROUP ACTIONS AND THE RIBAUCOUR TRANSFORMATIONS FOR FLAT LAGRANGIAN SUBMANIFOLDS[J].Chinese Annals of Mathematics,Series B,2005,26(3):347-360.
-
6本刊编辑部.拉格朗日子流形的若干问题[J].信阳师范学院学报（自然科学版）,2013,26(4).
-
7杨标桂,朱晴晴.近Kaehler流形S^3×S^3上的殆切触拉格朗日子流形[J].纯粹数学与应用数学,2014,30(5):454-459. 被引量：1
-
8韩冰,曾可依.复格拉斯曼流形G(2,4)中的一族拉格朗日S^3×T^1[J].合肥工业大学学报（自然科学版）,2014,37(7):893-896. 被引量：1
-
9Robert L. BRYANT.SO(n)-Invariant Special Lagrangian Submanifolds of C^(n+1) with Fixed Loci[J].Chinese Annals of Mathematics,Series B,2006,27(1):95-112.
-
10王宝勤,陈春丽.用含核子流形构造Lagrange子流形[J].工程数学学报,1997,14(4):97-101.
