| Chen Bang-yen | |
| Native Name: | 陳邦彦 |
| Native Name Lang: | Chinese |
| Birth Date: | 3 October 1943 |
| Birth Place: | Toucheng, Yilan, Taiwan |
| Nationality: | Taiwanese, American |
| Fields: | Differential geometry, Riemannian Geometry, Geometry and topology |
| Workplaces: | Michigan State University |
| Alma Mater: | Tamkang University, National Tsing Hua University, University of Notre Dame |
| Thesis Title: | On the G-total curvature and topology of immersed manifolds |
| Doctoral Advisor: | Tadashi Nagano |
| Doctoral Students: | Bogdan Suceavă |
| Known For: | "Chen inequalities", "Chen invariants (or δ-invariants)", "Chen's conjectures", "Chen surface", "Chen–Ricci inequality", "Chen submanifold", "Chen equality", "Submanifolds of finite type", "Slant submanifolds", "ideal immersion", "(M+,M-)-theory for compact symmetric spaces & 2-numbers of Riemannian manifolds (joint with Tadashi Nagano)". |
| Children: | Three Children - Two Girls, One Boy |
Chen Bang-yen is a Taiwan-born mathematician who works mainly on differential geometry and related subjects. He was a University Distinguished Professor of Michigan State University from 1990 to 2012. After 2012 he became University Distinguished professor emeritus.
Chen Bang-yen (陳邦彦) is a Taiwanese-American mathematician. He received his B.S. from Tamkang University in 1965 and his M.Sc. from National Tsing Hua University in 1967. He obtained his Ph.D. degree from University of Notre Dame in 1970 under the supervision of Tadashi Nagano.[1] [2]
Chen Bang-yen taught at Tamkang University between 1965 and 1968, and at the National Tsing Hua University in the academic year 1967–1968. After his doctoral years (1968-1970) at University of Notre Dame, he joined the faculty at Michigan State University as a research associate from 1970 to 1972, where he became associate professor in 1972, and full professor in 1976. He was presented with the title of University Distinguished Professor in 1990. After 2012 he became University Distinguished Professor Emeritus.[3] [4] [5]
Chen Bang-yen is the author of over 570 works including 12 books, mainly in differential geometry and related subjects. He also co-edited four books, three of them were published by Springer Nature and one of them by American Mathematical Society.[6] [7] His works have been cited over 36,000 times.[8] He was named as one of the top 15 famous Taiwanese scientists by SCI Journal.[9]
On October 20–21, 2018, at the 1143rd Meeting of the American Mathematical Society held at Ann Arbor, Michigan, one of the Special Sessions was dedicated to Chen Bang-yen's 75th birthday.[10] [11] The volume 756 in the Contemporary Mathematics series, published by the American Mathematical Society, is dedicated to Chen Bang-yen, and it includes many contributions presented in the Ann Arbor event.[12] The volume is edited by Joeri Van der Veken, Alfonso Carriazo, Ivko Dimitrić, Yun Myung Oh, Bogdan Suceavă, and Luc Vrancken.
On July 15-16, 2024, within the 9th European Congress of Mathematics, the mini-symposium MS-8 was dedicated to the Geometry of Submanifolds. In celebration of Bang-Yen Chen's 80th Birthday. The mini-symposium was organized by Alfonso Carriazo, Bogdan Suceavă, and Mihaela Vajiac, and the contributors were W.G. Boskoff, Pablo Alegre, Anna Maria Candela, Alfonso Carriazo, Mirjana Djoric, Ildefonso Castro, Adela Mihai, Joeri Van der Veken, Alvaro Pampano, and Bogdan Suceavă.
Given an almost Hermitian manifold, a totally real submanifold is one for which the tangent space is orthogonal to its image under the almost complex structure. From the algebraic structure of the Gauss equation and the Simons formula, Chen and Koichi Ogiue derived a number of information on submanifolds of complex space forms which are totally real and minimal. By using Shiing-Shen Chern, Manfredo do Carmo, and Shoshichi Kobayashi's estimate of the algebraic terms in the Simons formula, Chen and Ogiue showed that closed submanifolds which are totally real and minimal must be totally geodesic if the second fundamental form is sufficiently small.[13] By using the Codazzi equation and isothermal coordinates, they also obtained rigidity results on two-dimensional closed submanifolds of complex space forms which are totally real.
In 1993, Chen studied submanifolds of space forms, showing that the intrinsic sectional curvature at any point is bounded below in terms of the intrinsic scalar curvature, the length of the mean curvature vector, and the curvature of the space form. In particular, as a consequence of the Gauss equation, given a minimal submanifold of Euclidean space, every sectional curvature at a point is greater than or equal to one-half of the scalar curvature at that point. Interestingly, the submanifolds for which the inequality is an equality can be characterized as certain products of minimal surfaces of low dimension with Euclidean spaces.
Chen introduced and systematically studied the notion of a finite type submanifold of Euclidean space, which is a submanifold for which the position vector is a finite linear combination of eigenfunctions of the Laplace-Beltrami operator. He also introduced and studied a generalization of the class of totally real submanifolds and of complex submanifolds; a slant submanifold of an almost Hermitian manifold is a submanifold for which there is a number such that the image under the almost complex structure of an arbitrary submanifold tangent vector has an angle of with the submanifold's tangent space.
In Riemannian geometry, Chen and Kentaro Yano initiated the study of spaces of quasi-constant curvature. Chen also introduced the δ-invariants (also called Chen invariants), which are certain kinds of partial traces of the sectional curvature; they can be viewed as an interpolation between sectional curvature and scalar curvature. Due to the Gauss equation, the δ-invariants of a Riemannian submanifold can be controlled by the length of the mean curvature vector and the size of the sectional curvature of the ambient manifold. Submanifolds of space forms which satisfy the equality case of this inequality are known as ideal immersions; such submanifolds are critical points of a certain restriction of the Willmore energy.
In the theory of symmetric spaces, Chen and Tadashi Nagano created the (M+,M-)-theory for compact symmetric spaces.[14] [15] One of advantages of their theory is that it is very useful for applying inductive arguments on polars or meridians.[16] [17]
Major articles
Surveys
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