基本信息

焦晓祥 男 汉族 博导 数学科学学院
电子邮件:xxjiao@ucas.ac.cnxxjiao@ucas.edu.cn
联系电话:010-69671488(雁栖湖校区);传真:010-69671499
通信地址:北京市怀柔区怀北镇怀北庄380号中国科学院大学雁栖湖校区数学科学学院
邮政编码:101408

部门/实验室:数学科学学院

研究领域

整体微分几何

招生信息

每年招收1--2名微分几何方向硕士、博士研究生,欢迎报考。
招生专业
070101-基础数学
070103-概率论与数理统计
招生方向
微分几何
统计推断与微分几何

教育背景

1995-02--1998-01 中国科学院大学,基础数学专业, 博士研究生
1985-09--1988-07 浙江大学数学系,基础数学专业, 硕士研究生
1981-09--1985-07 南昌大学数学系,基础数学专业, 本科
学历
中科院研究生院 -- 研究生
学位
中科院研究生院 -- 博士

工作经历

2003-12--2004-11,德国Regensburg大学数学系,助教;
2002-07--2003-01,台湾中央研究院数学研究所,访问;
2001-08至今,中国科学院大学,教师;
1999-09--2001-08,中国科学院数学与系统科学研究院数学研究所,博士后;
1988-07--1999-12,南昌大学数学系,教师。


教授课程

微分几何Ⅰ、 微分几何选读、 微分几何Ⅱ、 微分几何II、 微分几何I、 复变函数与积分变换、 微分几何、 积分变换、 复变函数、 黎曼曲面

论文目录

主要论文目录:
[1]
空间形式中具有三个互异主曲率的超曲面,杭州大学学报,17(3)(1990 ),271-279.

[2] Conformal minimal two-spheres with constant Gauss curvature in U(3),Chinese Science Bulletin,43(12)(1998 ), 994-997.

[3]曲面到U(N)中有限的调和映射,数学进展,27(6)(1998),533—535. doi: 10.11845/sxjz.1998.27.06.0533.

[4]关于曲面到U(N)的调和映射的极小Uniton数,数学杂志,19(4)(1999),368--370。

[5] On conformal minimal Immersions of two-spheres in CP^N, Journal of Mathematical Reasearch Exposition, 20(2) (2000), 201--205. Article ID: 1000-341X(2000)02-0201-05.

[6] On factorization of harmonic maps of surfaces into U(N) and a ction of groups, Northeastern Mathematical Journal(东北数学),16(2)(2000), 160--166. Article ID : 100021778 (2000) 0220160207.

[7]在调和映射空间上的Dressing作用,中国科学院研究生院学报,17(1)(2000),8--12。

[8]关于从曲面到复Grassmann流形中的调和映射,数学年刊(A辑),21A(1)(2000),57--60。

[9] Factorization of harmonic maps of surfaces into lie groups by singular dressing action. Differential Geometry and Integrable Systems (Tokyo, 2000), 199--204,Contemp. Math., 308, Amer. Math. Soc., Prvidence, RI, 2002.

[10] On non-isotropic harmonic maps of surfaces into complex projective spaces (with Peng Jiagui), Science in China, Ser. A, 44(5)(2001), 555--561. DOI: 10.1007/BF02876703.

[11] The isoenergy inequality for harmonic maps from rotational symmetric manifolds (with Li Jiayu), Journal of Partial Differential Equations, 15(1)(2002), 1--6.

[12] Rigidity of holomorphic curves in complex Grassmann manifolds (with Peng Jiagui), Mathematische Annalen, 327(3)(2003), 481--486. DOI: 10.1007/s00208-003-0462-5.

[13] Pseudo-holomorphic curves in complex Grassmann manifolds (with Peng Jiagui), Transactions of the American Mathematical Society, 355(9)(2003), 3715--3726. DOI:10.1090/S0002-9947-03-03244-6.

[14] Classification of holomorphic spheres of constant curvature in complex Grassmann maniofolds G(2,5) (with Peng Jiagui), Differential Geometry and Its Applications, 20(3)(2004), 267--277. doi:10.1016/j.difgeo.2003.10.011.

[15] Curve shortening flow in arbitary dimensional eucldian space (with Yang Yunyan), Acta Mathematica Sinica, English Series, 21(4) (2005), 715--722. DOI: 10.1007/s10114-004-0426-z.

[16] Minimal 2-spheres in a complex projective space (with Peng Jiagui), Differential Geometry and its Applications, 25(5)(2007), 506--517. doi: 10.1016/j.difgeo.2007.06.002.

[17] Pseudo-holomorphic curves of constant curvature in complex Grassmannians, Israel Journal of Mathematics, 163(1)(2008), 45--63. DOI: 10.1007/s11856-008-0003-8.

[18] Holomorphic two-spheres in complex Grassmann manifold G(2,4) (with Xu Xiaowei), Proc. Indian Acad. Sci.-Math. Sci,118(3)(2008), 381--388. DOI 10.1007/s12044-008-0030-8.

[19] Conformal minimal immersions of S^2 in CP^n (with Chen Hongxia), 中国科学院研究生院学报, 25(4)(2008), 452--459. Article ID: 1002-1175(2008)04-0452-08.

[20] On minimal two-spheres in G(2, 4) (with Peng Jiagui), Front Math China, 5(2)(2010), 297--310. DOI 10.1007/s11464-010-0009-5.

[21] On pseudo-holomorphic curves from two-spheres into a complex Grassmannian G(2,5), Acta Mathematica Sinica, 26(4)(2010), 759--762. DOI: 10.1007/s10114-010-7262-0.

[22] On some conformal minimal two-spheres in a complex projective space (with Peng Jiagui), Quarterly Journal of Mathematics, 61(1)(2010), 87--101. doi:10.1093/qmath/han029.

[23] Conformal minimal two-spheres in Q_n (with Wang Jun), Science China Mathematics, 54(4)(2011), 817--830. doi: 10.1007/s11425-011-4179-8.

[24] Conformal minimal two-spheres in Q_2 (with Wang Jun), Frontiers of Mathematics in China, 6(3)(2011), 535--544. DOI 10.1007/s11464-011-0137-6.

[25] On holomorphic curves in a complex Grassmann manifold G(2,n) (with Yu Yan), Archiv der Mathematik, 96(3)(2011), 291--300. DOI 10.1007/s00013-011-0231-8.

[26] On holomorphic curves of constant curvature in a complex Grassmann manifold G(2,5) (with Peng Jiagui), Acta Mathematica Scientia, 31B(1) (2011), 237--248. DOI: 10.1016/S0252-9602(11)60224-5.

[27] Holomorphic 2-spheres in a complex Grassmann manifold G(2,5) (with Fei Jie), Journal of the Graduate School of the Chinese Academy of Sciences, 28(2)(2011), 131--140. Article ID: 1002-1175(2011)02-0131-10.

[28] Construction of homogenous minimal 2-spheres in complex Grassmannians (with Fei Jie & Xu Xiaowei), Acta Mathematica Scientia, 31B(5)(2011), 1889--1898. DOI: 10.1016/S0252-9602(11)60368-8.

[29] On conformal minimal 2-spheres in complex Grassmann manifold G(2,n) (with Fei Jie & Xu Xiaowei), Proc. Indian Acad. Sci. (Math. Sci.),121(2)(2011), 181--199. DOI 10.1007/s12044-011-0019-6.

[30] Harmonic two-spheres in the complex Grassmann manifold G(2,5) (with Li Kang), 中国科学院研究生院学报, 28(5)(2011), 573--582. Article ID: 1002-1175(2011)05-0573-10.

[31] SU(2)-orbits in a six-sphere (with Zhou Xianchao), Journal of Graduate University of Chinese Academy of Sciences, 29(1)(2012), 1--11. Article ID: 1002-1175(2012)01-00-11.

[32] On almost complex curves in the nearly kaehler six-sphere (with Zhou Xianchao), Differential Geometry and its Applications, 30(2)(2012), 148--152. doi:10.1016/j.difgeo.2012.01.002.

[33] On minimal two-spheres immersed in complex Grassmann manifolds with parallel second fundamental form, Monatshefte für Mathematik, 168(3-4)(2012), 381--401. DOI 10.1007/s00605-012-0403-z.

[34] Holomorphic two-spheres in the complex Grassmann manifold G(k,n) (with Zhong Xu and Xu Xiaowei), Proceedings Mathematical Sciences, 122(3)(2012), 399-409.DOI 10.1007/s12044-012-0084-5.

[35]Langrangian submanifolds in complex projective space $CP^n$ (with Peng Jiagui, Xu Xiaowei), Frontiers of Mathematics in China, 7(6)(2012), 1129--1140. DOI 10.1007/s11464-012-0244-z.

[36] The Classification of homogeneous 2-spheres in complex Grassmannians (with Fei Jie, Xiao Liang, Xu Xiaowei), Osaka Journal of Mathematics, 50(1)(2013), 135-152. Project Euclid: euclid.ojm/1364390422.

[37] Minimal surfaces in a complex hyperquadric Q_2 (with Wang Jun),Manuscripta Mathematica, 140(3-4)(2013), 597-611. DOI: 10.1007/s00229-012-0554-1.

[38]Totally real minimal surfaces in the complex hyperquadrics (with Wang Jun), Differential Geometry and its Applications, 31(4)(2013), 540-555. DOI 10.1016/j.difgeo.2013.05.007.

[39] Totally real conformal minimal Tori in the hyperquadric $Q_2$ (with Zhong Xu and Wang Jun), Science China Mathematics, 56(10)(2013), 2015--2023. doi: 10.1007/s11425-013-4600-6.

[40] On almost complex curves and Hopf hypersufaces in the nearly Kaehler six-sphere (with He Ling and Zhou Xianchao), Science China Mathematics, 57(5)(2014), 1045-1056. doi: 10.1007/s11425-014-4777-3.

[41] Classification of conformal minimal immersions of constant curvature from $S^2$ to $HP^2$ (with He Ling), Mathematische Annalen, 359(3-4)(2014), 663-694. DOI 10.1007/s00208-014-1013-y.

[42] On conformal minimal immersions of $S^2$ in $HP^n$ with parallel second fundamental form (with He Ling), Annali di Matematica Pura ed Applicata, 194(5)(2015), 1301—1317. DOI 10.1007/s10231-014-0420-8.

[43]  On conformal minimal immersions of constant curvature from S^2 to HP^n (with He Ling), Mathematische Zeitschrift, 280(3-4)(2015), 851-871. DOI 10.1007/s00209-015-1452-5.

[44] Rigidity of holomorphic curves of constant curvature in G(2,5)(with He Ling), Differential Geometry and its Applications, 43(2015), 21-44. 

[45] On conformal minimal immersions of two-Spheres in a complex Hyperquadric with parallel second fundamental form (with Li Mingyan), The Journal of Geometric Analysis, 26(1)(2016), 185--205. DOI 10.1007/s12220-014-9544-8.

[46] Classification of conformal minimal immersions of constant curvature from S^2 to Q_3, The journal of the Mathematical Society of Japan, 68(2)(2016), 863--883.

[47] Jiao Xiaoxaing and Li Mingyan, Minimal surfaces in symmetric spaces with parallel second fundamental form, Proceedings Mathematical Sciences, 127(2017), 719-735.

[48] Jiao Xiaoxiang and Li Mingyan, Classification of conformal minimal immersions of constant curvature from S^2 to Q_n, Annali di Matematica Pura ed Applicata, 196(2017), 1001-1023.

[49] Chen Xiaodong and Jiao Xiaoxiang*, Conformal minimal surfaces immersed into HP^n, Annali di Matematica Pura ed Applicata, 196(6)(2017), 2063-2076.

[50] 焦晓祥,徐言,复Grassmann流形中的实迷向极小二维球面,中国科学:数学,477)(2017),827—840.

 

 

 


 

科研活动

科研项目:

(1)极小子流形的几何(国家自然科学基金面上项目,批准号:11871450),主持,2019.01--2022.12;
(2)Riemann面上奇异与非奇异共形度量(国家自然科学基金面上项目,批准号:11471308) ,参与,2015.01--2018.12;
(3) 子流形的几何与拓扑(国家自然科学基金重点项目,No. 11331002),主持(子课题),2014.01--2018.12 ;
(4) 对称空间中的极小曲面的几何(国家自然科学基金面上项目, No. 11071248),主持,2011.01--2013.12 ;
(5) 数学物理中的若干重大问题(中科院知识创新项目, No. KJCX3-SYW-S03),主持(子课题),2007.01--2010.12 ;
(6) 极小曲面的几何(教育部留学回国人员科研启动基金,No. [2006]331),主持,2006.11--2008.10 ;
(7) 调和映射的几何(国家自然科学基金重点项目, No. 10531090),主持(子课题),2006.01--2009.12;
(8) 几何与数学物理的若干问题(中科院知识创新项目),主持(子课题),2004.05--2006.04;
(9) 微分几何的若干问题与可积系统方法(国家自然科学基金面上项目,No. 10071804),参与,2001.01--2003.12;
(10) 调和映射与环群理论(国家自然科学基金, No. 10001033),主持,2001.01--2003.12。

指导学生

已毕业学生:
博士:许小卫(硕博连读,2004年9月-2009年7月),王军(硕博连读,2006年9月-2011年7月),费杰(2008年9月-2011年7月),周显潮(硕博连读,2007年9月-2012年7月),钟旭(2010年9月-2013年7月),何玲(硕博连读,2009年9月-2014年7月),李明艳(硕博连读,2010年9月-2015年7月),陈晓东(硕博连读,2012年9月-2017年7月),张文娟(2014年9月-2017年7月),魏志强(2015年9月-2018年7月),李虹(2016年9月-2019年7月)。
硕士:陈红霞(2005年9月-2008年7月),李康(2008年9月-2011年7月),徐言(2014年9月-2017年7月),高紫娟(2015年9月-2018年7月),崔洪斌(2016年9月-2019年7月)。

在读学生:
博士:徐言,崔洪斌。

硕士:辛嘉麟,张少腾,于文浩。