Background
Chen, Bang-Yen was born on October 3, 1943 in Yilan, Taiwan.
2001
Tokyo, Japan
With Koichi Ogiue (left).
2003
Michigaan State University, East Lansing, MI
With Sir Michael F. Atiyah (right)
(The first two chapters of this frequently cited reference...)
The first two chapters of this frequently cited reference provide background material in Riemannian geometry and the theory of submanifolds. Subsequent chapters explore minimal submanifolds, submanifolds with parallel mean curvature vector, conformally flat manifolds, and umbilical manifolds. The final chapter discusses geometric inequalities of submanifolds, results in Morse theory and their applications, and total mean curvature of a submanifold. Suitable for graduate students and mathematicians in the area of classical and modern differential geometries, the treatment is largely self-contained. Problems sets conclude each chapter, and an extensive bibliography provides background for students wishing to conduct further research in this area. This new edition includes the author's corrections.
2019
(During the last four decades, there were numerous importa...)
During the last four decades, there were numerous important developments on total mean curvature and the theory of finite type submanifolds. This unique and expanded second edition comprises a comprehensive account of the latest updates and new results that cover total mean curvature and submanifolds of finite type. The longstanding biharmonic conjecture of the author's and the generalized biharmonic conjectures are also presented in details. This book will be of use to graduate students and researchers in the field of geometry. Readership: Researchers and graduate students in geometry.
http://www.amazon.com/gp/product/9814616680/?tag=2022091-20
(The purpose of this book is to introduce the reader to tw...)
The purpose of this book is to introduce the reader to two interesting topics in geometry which have developed over the last fifteen years, namely, total mean curvature and submanifolds of finite type. The theory of total mean curvature is the study of the integral of the n-th power of the mean curvature of a compact n-dimensional submanifold in a Euclidean m-space and its applications to other branches of mathematics. The relation of total mean curvature to analysis, geometry and topology are discussed in detail. Motivated from these studies, the author introduces and studies submanifolds of finite type in the last chapter. Some applications of such submanifolds are also given. This book is self-contained. The author hopes that the reader will be encouraged to pursue his studies beyond the confines of the present book.
http://www.amazon.com/gp/product/9971966034/?tag=2022091-20
(A warped product manifold is a Riemannian or pseudo-Riema...)
A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson Walker models, are warped product manifolds. The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson Walker's and Schwarzschild's. The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century. The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.
http://www.amazon.com/gp/product/9813208929/?tag=2022091-20
陳邦彦
Chen, Bang-Yen was born on October 3, 1943 in Yilan, Taiwan.
Bachelor of Science, Tamkang U., Taipei, Taiwan, 1965;
Master of Science, Tsinghua U., Hsinchu, Taiwan, 1967;
Doctor of Philosophy, U. Notre Dame, Indiana, 1970;
Doctor of Science, Science University of Tokyo, 1982.
Instructor, Tamkang U., Taipei, 1966-1968;
instructor, Tsinghua U., Hsinchu, 1967-1968;
research associate, Michigan State University, East Lansing, 1970-1972;
associate professor mathematics, Michigan State University, East Lansing, 1972-1976;
professor, Michigan State University, East Lansing, 1976-1990;
University Distinguished professor, Michigan State University, East Lansing, since 1990.
(A warped product manifold is a Riemannian or pseudo-Riema...)
(The purpose of this book is to introduce the reader to tw...)
(During the last four decades, there were numerous importa...)
Geometry of Submanifolds - Dover Edition
(The first two chapters of this frequently cited reference...)
2019Correspondent member of Accademia Peloritana, Italy.
Married Pi-Mei Chang, September 5, 1968. Three adult children and six grandchildren.