研究領(lǐng)域
主要從事李理論與微分幾何、李群表示理論等的研究。主要科研成果包括：構(gòu)造出第一個李代數(shù)上非對稱雙極化的例子，解決了日本數(shù)學家金行壯二提出的待解問題；系統(tǒng)研究了齊性仿凱勒流形的幾何性質(zhì)，最終得到了半單情形的代數(shù)分類，這一領(lǐng)域的成果被金行壯二教授稱贊為“輝煌的結(jié)果”，并兩次在日本數(shù)學會年會上報告；決定了李群表示理論中一類最高權(quán)向量環(huán)的全部關(guān)系，瑞典的審稿人評價此結(jié)果“非常令人佩服”；利用李理論，系統(tǒng)研究了芬斯勒幾何的等距變換群和齊性、對稱Finsler空間，相關(guān)結(jié)果被審稿人評價為“具有國際競爭力”，“是對Finsler幾何的重要貢獻”，F(xiàn)insler幾何的權(quán)威，美國印地安娜大學沈中民教授在美國數(shù)學評論上評論我們的結(jié)果“opens a door to using Lie group theory to study Finsler geometry”。已發(fā)表論文二十多篇。
主要成就
主持過國家自然科學基金青年項目，國家自然科學基金面上項目。1999年與侯自新教授合作的項目《齊性仿凱勒流形的幾何》獲教育部科技進步三等獎。2003年入選“教育部優(yōu)秀青年教師資助計劃”，2004年入選首屆“新世紀優(yōu)秀人才支持計劃”。
發(fā)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.
