邓少强(南开教授)

时间:2023-12-18 08:18:56编辑:小周

邓少强(南开教授)的个人简介

邓少强,1965年12月生,湖南人。1988年本科毕业于湘潭大学数学系,同年进入南开大学数学研究所学习,1991年获理学硕士学位;1995年起在职攻读博士学位,1998年获理学博士学位。现为南开大学基础数学教授,博士生导师。

研究领域

主要从事李理论与微分几何、李群表示理论等的研究。主要科研成果包括:构造出第一个李代数上非对称双极化的例子,解决了日本数学家金行壮二提出的待解问题;系统研究了齐性仿凯勒流形的几何性质,最终得到了半单情形的代数分类,这一领域的成果被金行壮二教授称赞为“辉煌的结果”,并两次在日本数学会年会上报告;决定了李群表示理论中一类最高权向量环的全部关系,瑞典的审稿人评价此结果“非常令人佩服”;利用李理论,系统研究了芬斯勒几何的等距变换群和齐性、对称Finsler空间,相关结果被审稿人评价为“具有国际竞争力”,“是对Finsler几何的重要贡献”,Finsler几何的权威,美国印地安娜大学沈中民教授在美国数学评论上评论我们的结果“opens a door to using Lie group theory to study Finsler geometry”。已发表论文二十多篇。

主要成就

主持过国家自然科学基金青年项目,国家自然科学基金面上项目。1999年与侯自新教授合作的项目《齐性仿凯勒流形的几何》获教育部科技进步三等奖。2003年入选“教育部优秀青年教师资助计划”,2004年入选首届“新世纪优秀人才支持计划”。

发表文章及著作:

1.S. Deng, Homogeneous Finsler spaces(Xii+232pages), to appear in the series: Springer monographs in mathematics, Springer, New York, 2012.

2.S. Deng, On the Symmetry of Riemannian manifolds, J. ReineAngew. Math., published online 2012, DOI: 10.1.15/ CRELLE.2012.040.

3.Z. Hu, S. Deng, Homogeneous Finsler spaces with isotropic S-curvature and positive flag curvature, Math. Zeitschrift, published online 2011,DOI: 10.1007

4.S. Deng, On the classification of weakly symmetric Finsler spaces, Israel Journal of Mathematics, 181 (2011), 29-52.

5.S. Deng, Z. Hou, On symmetric Finsler spaces, Israel Journal of Mathematics, 162 (2007), 197-219.

6.S. Deng, Finsler metrics and the degree of symmetry of a closed manifold, Indiana University Mathematics Journal, accepted 2010.

7.S. Deng, Z. Hou, Homogeneous Einstein-Randers spaces of negative Ricci curvature, C. R. Math. Acad. Sci. Paris, Ser. I 347 (2009), 1169-1172.

8.S. Deng, Invariant Finsler metrics on polar homogeneous manifolds, Pacific Journal of Mathematics, 247 (2011), 47-74.

9.S. Deng, Z. Hou, Weakly symmetric Finsler spaces, Communications in Contemporary Mathematics, 12 (2010), 309-323.

10.S. Deng, M. Xu, Clifford-Wolf translations of Finsler spaces, Forum Mathematicum, accepted.

11.S. Deng, An algebraic approach to weakly symmetric Finsler spaces, Canadian Journal of Mathematics, 62 (2010), 52-73.

12.S. Deng, Z. Hu, On flag curvature of homogeneous Randers spaces, Canadian Journal of Mathematics, published online 2012, DOI: 10.4153/CJM-2012-004-6.

13.H. Wang, S. Deng, Some homogeneous Enistein-Randers spaces, Nonlinear Analysis, 72(2010), 4407-4414.

14.H. Wang, L. Huang, S. Deng, Homogeneous Einstein-Randers metrics on spheres, Nonlinear Analysis, 74 (2011), 6291-6301.

15.Z. Hu, S. Deng, Three dimensional homogeneous Finsler spaces, Math. Nachr., published online, 2012, DOI: 10.1002/mana.201100100.

16.H. Wang, S. Deng, Left invariant Einstein-Randers metrics on compact Lie groups, Canadian Math. Bull., Published online 2011/DOI: 10-4153/CMB-2011-145-6.

17.S. Deng, X. Wang, The S-curvature of homogeneous (α,β)-metrics, Balkan Journal of Geometry and its Applications, 15 (2010), no.2, 47-56..

18.S. Deng, Z. Hou, Naturally reductive homogeneous Finsler spaces, ManuscriptaMathematica, 131 (2010), 215-229.

19.J. Lin, Y. Wang, S. Deng, T*-extension of Lie triple systems, Linear Algebra and its Applications, 431 (2009), 2071-2083.

20.S. Deng, The S-curvature of homogeneous Randers spaces, Differential Geometry and its Applications, 27 (2009), 75-84.

21.Y. Wang, J. Lin and S. Deng, Solvable Lie algebras with quasi-filiformnilradicals, Communications in Algebra, 36 (2008), 4052-4067.

22.S. Deng, Z. Hou, Positive definite Minkowski Lie algebras and bi-invariant Finsler metrics on Lie groups, GeometriaeDedicata, 136 (2008), 191-201.

23.H. An and S. Deng, Invariant (α,β)-metrics on homogeneous manifolds, MonatsheftefürMathematik, 154 (2008), 89-102.

24.S. Deng, Fixed points of isometries of a Finsler space, Publ. Math. Debrecen, 72 (2008), 469-474.

25.S. Deng, Z. Hou, Homogeneous Finsler spaces of negative curvature, Journal of Geometry and Physics, 57 (2007), 257-264.

26.S. Deng, Z. Hou, Invariant Finsler metrics on homogeneous manifolds II: complex structures, J. Physics A-Math. Gen., 39 (2006), 2599-2609.

27.S. Deng, Z. Hou, Minkowski symmetric Lie algebras and symmetric Berwald spaces, GeometriaeDedicata, 113 (2005), 95-105.

28.S. Deng, Z. Hou, On locally and globally symmetric Berwald spaces, Journal of Physics A: Mathematical and General, 38 (2005), 1691-1697.

29.S. Deng, Z. Hou, Invariant Finsler metrics on homogeneous manifolds, Journal of Physics A: Mathematical and General, 37 (2004), 8245-8253.

30.S. Deng, Z. Hou, Invariant Randers metrics on homogeneous Riemannian manifolds, Journal of Physics A: Mathematical and General, 37 (2004), 4353-4360.

31.S. Deng, Z. Hou, The group of isometries of a Finsler space, Pacific Journal of Mathematics, 207 (2002), 149-155.

32.S. Deng, Z. Hou, The ideal of relations of certain rings of highest weight vectors, Algebra Colloquium, 8 (2001), 275-284.

33.S. Deng, Z. Hou, Stability of certain rings of highest weight vectors, Chin. Ann. Math. B, 22(2001), 57-62.

34.Z. Hou, S. Deng, S. Kaneyuke, K. Nishiyama, Dipolarizations in semisimple Lie algebras and homogeneous parakaehler manifolds, Journal of Lie Theory, 9 (1999), 215-232.

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