基本信息

姓名：程新跃

职称：教授

系部： 数学系

办公室： 数学系212

办公电话：13527501832

Email： chengxy@cqnu.edu.cn 

 

社会兼职：

历任重庆市数学会副理事长，重庆欧美同学会第一、二届理事会理事, 欧美同学会中东欧分会理事。

 

研究方向： 整体微分几何

 

主讲课程：

先后为本科生主讲《高等代数》、《解析几何》、《微分几何》、《高等几何》、《概率论与数理统计》等课程；先后为研究生主讲《现代几何基础》、《现代芬斯勒几何》、《整体芬斯勒几何》、《芬斯勒几何及其应用》、《拓扑学基础》、《信息几何学》等课程。

代表论著：

已在国内外重要学术刊物发表论文90余篇；由德国Springer出版社与科学出版社联合出版学术专著（英文）一部；由科学出版社出版研究生教材一部。

1. 著作

   [1] (with Zhongmin Shen) Finsler Geometry -- An Approach via Randers Spaces, Springer, Heidelberg and Science Press, Beijing, 2012.

   [2] 程新跃，李体耀，现代几何基础，科学出版社，北京，2020.

2. 论文

   [1] (with Y. Feng) Some functional inequalities and their applications on Finsler measure spaces, The Journal of Geometric Analysis, 34 (2024): 127.

   [2] (with H. Cheng) The characterizations on a class of weakly weighted Einstein-Finsler metrics, The Journal of Geometric Analysis，33(2023) : 267.

   [3] (with K. Cao and C. Qing) The characterizations and constructions of  sprays of isotropic curvature, Acta Mathematica Sinica, 38(9)(2022), 1612-1620.

   [4] Gradient estimates for positive solutions of heat equations under Finsler-Ricci flow, Journal of Mathematical Analysis and Applications, 508(2)(2022): 125897.

   [5] (with Z. Shen) Some inequalities on Finsler manifolds with weighted Ricci curvature bounded below, Results in Mathematics, 77(2022): 70.

   [6] (with G. Chen ) On (alpha,beta)-metrics of constant flag curvature, Acta Mathematica Scientia, 42B(2)(2022), 755–768.

   [7] (with Y. Gong) Randers metrics with isotropic scalar curvature, Acta Mathematica Sinica (Chinese Series), , 64(6)(2021), 1027- 1036.

   [8] (with Q. Qu and S. Xu) The navigation problems on a class of conic Finsler manifolds，Differential Geometry and its Applications，74 (2021): 101709.

   [9] (with L. Yin and T. Li) A class of Randers metrics of scalar flag curvature, International Journal of Mathematics, 31(13)(2020): 2050114.

   [10] (with G. Chen) Projectively flat singular square metrics with constant flag curvature, Acta Mathematica Sinica，36(6)(2020), 638-650.n

   [11] (with Q. Huang and S. Wu) The conformal invariances of the dually flat (α, β)-metrics, Acta Mathematica Sinica (Chinese Series), 62(3)(2019), 397-408.

   [12] (with T. Li and L. Yin) The conformal vector fields on conic Kropina manifolds via navigation data, Journal of Geometry and Physics, 131(2018), 138-146.

   [13] (with L. Yin and T. Li) The conformal vector fields on Kropina  manifolds, Differential Geometry and Its Applications, 56(2018), 344-354.

   [14] (with Z. Shen and G. Yang) On a class of two-dimensional Finsler manifolds of isotropic S-curvature, SCIENCE CHINA Mathematics, 61(1)(2018), 57-72.

   [15] Hilbert's fourth problem and projectively flat Finsler metrics, Lie groups, Differential equations, and Geometry, Advances and Surveys, Edited by Giovanni Falcone, Springer, 2017, 247-263.

   [16] (with Y. Shen and X. Ma) On a class of projective Ricci flat Finsler metrics, Publications Mathematicae Debrecen, 90/1-2(2017), 169-180.

   [17] (with Z. Shen) Einstein Finsler metrics and Killing vector fields on Riemannian manifolds, SCIENCE CHINA Mathematics, 60(1)(2017), 83-98.

   [18] (with M. Yuan) On conformally flat (α, β)-metrics with special curvature properties,  Acta Mathematica Sinica, 31(5)(2015), 879–892.

   [19] The (α, β)-metrics of scalar flag curvature, Differential Geometry and its Applications, 35(2014), 361-369.

   [20] (with H. Li and Y. Zou) On conformally flat (α, β)-metrics with relatively isotropic mean Landsberg curvature, Publications Mathematicae Debrecen, 85/1-2(2014), 131- 144.  

   [21] (with G. Chen) On an important non-Riemannian quantity in Finsler geometry, Results in Mathematics, 65(2014), 491-499.

   [22] (with M. Yuan) On Randers metrics of isotropic scalar curvature, Publications Mathematicae Debrecen, 84/1-2 (2014), 63-74.

   [23] (with Y. Zou) The generalized unicorn problem on (α, β)-metrics, Journal of Mathematical Analysis and Applications, 414(2014), 574-589.

   [24] (with G. Chen and M. Yuan) On a class of projectively flat Finsler metrics with weakly isotropic flag curvature, Periodica Mathematica Hungarica, 67(2)(2013), 155-166.

   [25] (with G. Chen) An important class of conformally flat weak Einstein Finsler metrics, International Journal of Mathematics, 24(1) (2013), 1350003(15 pages).

   [26] (with G. Chen and Y. Zou) On conformal transformations between two (α, β)-metrics,  Differential Geometry and Its Applications, 31(2013), 300–307.

   [27] (with Z. Shen and Y. Tian)  A class of Einstein (α, β)-metrics, Israel Journal of Mathematics, 192 (2012), 221–249.

   [28] The Ricci curvature in Finsler geometry, Recent Development in Geometry and Analysis, Advanced Lectures in Mathematics, 23, Edited by Yuxin Dong ects., Higher Education Press, 2012, 63-77.

   [29] (with G. Chen)  A class of Finsler metrics projectively related to a Randers metric, Publications Mathematicae Debrecen, 81/3-4(2012), 351-363.

   [30] (with G. Yang) Conformal invariances of two-dimensional Finsler spaces with isotropic main scalar, Publications Mathematicae Debrecen, 81/3-4(2012), 327-340.

   [31] (with Y. Tian) Ricci-flat Douglas (α, β)-metrics, Differential Geometry and its Applications, 30(2012), 20-32.

   [32] (with Y. Tian) Locally dually flat Finsler metrics with special curvature properties, Differential Geometry and its Applications, 29 (2011) , 98–106.

   [33] On (α, β)-metrics of scalar flag curvature with constant S-curvature, Acta Mathematica Sinica,  26(9)(2010), 1701-1708.

   [34] (with Z. Shen and Y. Zhou) On locally dually flat Finsler metrics, International Journal of Mathematics, 21(11)(2010), 1531-1543.

   [35] (with Z. Shen) Randers metrics of scalar flag curvature,  Journal of the Australian  Mathematical Society, 87(3)( 2009), 359-370.

   [36] (with Z. Shen) A class of Finsler metrics with isotropic S-curvature, Israel Journal of Mathematics，169(1)(2009), 317-340.

   [37] (with G. Yang) On generalized Einstein metrics in Finsler geometry, Publications Mathematicae Debrecen, 74/1-2(2009), 171-185.

   [38] (with H. Wang and M. Wang) (α, β)-metrics with relatively isotropic mean Landsberg curvature, Publications Mathematicae Debrecen, 72/3-4(2008), 475-485.

   [39] (with T. Q. Binh)  On a class of projectively flat  (α, β)-Finsler  metrics, Publication Mathematicae Debrecen,73/3-4 (2008), 391-400.

   [40] (with S. Bacso) Finsler conformal transformations and the curvature invariances, Publication Mathematicae Debrecen , 70/1-2(2007), 221-231.

   [41] (with M. Li) On a class of projectively flat (α,β)-metrics,  Publication Mathematicae Debrecen , 71/1-2 (2007), 195-205.

   [42] (with S. Bacso and Z. Shen) Curvature properties of (α, β)-metrics,Advanced Studies in Pure Mathematics, Math. Soc. of Japan，48(2007), 73-110.

   [43] (with Z. Shen) Projectively flat Finsler metrics with almost isotropic S-curvature,  Acta Mathematica Scientia，26B(2) (2006), 307-313.  

   [44] (with Z. Shen) On Douglas metrics, Publication Mathematicae Debrecen, 66(3-4) (2005), 503-512.

   [45] (with Z. Shen) Finsler metrics with special curvature properties, Periodica Mathematica Hungarica , 48(1-2)(2004), 33-47.

   [46] (with Z. Shen) A comparison theorem on the Ricci curvature in projective geometry, Annals of Global Analysis and Geometry, 23(2)(2003), 141-156.

   [47] (with Z. Shen) Randers metrics with special curvature  properties, Osaka Journal of Mathematics, 40(1)(2003), 87-101.

   [48] (with X. Mo and Z. Shen) On the flag curvature of Finsler metrics of scalar curvature, Journal of the London Mathematical Society, 68(2)(2003), 762-780.

   [49] (with W. Yang) The characteristics of hyperspheres in Minkowski spaces, Acta Mathematica Scientia，23B(1)(2003), 139-144.

   [50] (with W. Yang) On the Chern connection of Finsler submanifolds, Acta Mathematica Scientia, 20B(4)(2000), 551-557.

    

    

主持项目：

1. 先后主持近十项国家自然科学基金项目；作为主要研究人员先后参与国家自然科学基金重大专项项目、科技部“中国-匈牙利政府间科技合作项目”、欧盟第七框架项目（Seventh Framework Programm）各一项。

   近年来主持的国家自然科学基金项目包括：

2. 芬斯勒流形上若干重要的整体几何问题研究, 国家自然科学基金（批准号：12371051），2024.01.

   --- 2027.12., 项目负责人

3. 芬斯勒几何中若干重要曲率性质及相关问题研究，国家自然科学基金（批准号：11871126），2019.01.--- 2022.12., 项目负责人

4. 芬斯勒几何中的黎曼曲率及相关问题研究，国家自然科学基金(批准号: 11371386) , 2014.1.--- 2017.12., 项目负责人

5. 芬斯勒几何中的旗曲率与Ricci曲率，国家自然科学基金（批准号：10971239），2010.1.---2012.12., 项目负责人

 

 

荣誉获奖：

1992年9月被重庆市教委等评为“重庆市优秀青年教师”; 1993年9月被四川省人民政府授予“四川省优秀教师”称号; 1997年3月被评为兵器工业总公司部级“中青年后备学科带头人”; 2003年2月入选重庆市教育委员会“优秀中青年骨干教师资助计划”; 2008年8月被评为重庆市学术技术带头人; 作为项目负责人的项目《芬斯勒几何中的曲率性质》获2010年度重庆市自然科学奖二等奖。