226 citations · 552 across the 58 of their papers we have counts for
31 papers · 1 filter
Lagrangian submanifolds with prescribed second fundamental form
Bang-Yen Chen, Joeri Van der Veken, Luc Vrancken
We classify Lagrangian submanifolds of complex space forms, whose second fundamental form can be written in a certain way, depending on a real parameter. For some special values of…
Geometric classifications of homogeneous production functions
Bang-Yen Chen, Gabriel Eduard Vilcu
In this paper, we completely classify homogeneous production functions with an arbitrary number of inputs whose production hypersurfaces are flat. As an immediate consequence, we o…
Classification of spherical Lagrangian submanifolds in complex Euclidean spaces
Bang-Yen Chen
An isometric immersion from a Riemannian -manifold into a Kähler -manifold is called {\it Lagrangian} if the complex structure of…
Totally geodesic submanifolds of symmetric spaces, III
Bang-Yen Chen, Pui-Fai Leung, Tadashi Nagano
One purpose of this article is to establish a general method to determine stability of totally geodesic submanifolds of symmetric spaces. The method is used to determine the stabil…
Minimal flat Lorentzian surfaces in Lorentzian complex space forms
Bang-Yen Chen
In this article we study minimal flat Lorentzian surfaces in Lorentzian complex space forms. First we prove that, for minimal flat Lorentzian surfaces in a Lorentzian complex form,…
Open problems and conjectures on submanifolds of finite type revisited
Bang-Yen Chen
Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject had been collected in author's book [Total mean curvature and sub…
Conformal mappings and first eigenvalue of Laplacian on surfaces
Bang-Yen Chen
In this note we give a simple relation between conformal mapping and the first eigenvalue of Laplacian for surfaces in Euclidean spaces.
Ideal hypersurfaces of Euclidean four-space
Bang-Yen Chen
The notion of ideal immersions was introduced by the author in 1990s. Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is a nice isometric immer…
A survey on Geometry of Slant Submanifolds
Bang-Yen Chen
The present volume is the written version of the series of lectures the author delivered at the Catholic University of Leuven, Belgium during the period of June-July, 1990. The mai…
Construction of Hamiltonian-stationary Lagrangian submanifolds of constant curvature in complex space forms $\tilde M^n(4\varepsilon)
Bang-Yen Chen
Lagrangian submanifolds of a Kaehler manifold are called Hamiltonian-stationary (or -stationary for short) if it is a critical point of the area functional restricted to compact…
Geometry of quasi-sum production functions with constant elasticity of substitution property
Bang-Yen Chen
A production function is called quasi-sum if there are strict monotone functions with such that The justification…
Dependence of the Gauss-Codazzi equations and the Ricci equation of Lorentz surfaces
Bang-Yen Chen
The fundamental equations of Gauss, Codazzi and Ricci provide the conditions for local isometric embeddability. In general, the three fundamental equations are independent for surf…
Classification of minimal Lorentz surfaces in indefinite space forms with arbitrary codimension and arbitrary index
Bang-Yen Chen
Since J. L. Lagrange initiated in 1760 the study of minimal surfaces of Euclidean 3-space, minimal surfaces in real space forms have been studied extensively by many mathematicians…
Lagrangian submanifolds in complex space forms satisfying an improved equality involving
Bang-Yen Chen, Alicia Prieto-Marín, Xianfeng Wang
It was proved in [8,9] that every Lagrangian submanifold of a complex space form of constant holomorphic sectional curvature satisfies the following opt…
Recent developments of biharmonic conjecture and modified biharmonic conjectures
Bang-Yen Chen
A submanifold of a Euclidean -space is said to be biharmonic if holds identically, where is the mean curvature vector field and $Δ…
A Wintgen type inequality for surfaces in 4D neutral pseudo-Riemannian space forms and its applications to minimal immersions
Bang-Yen Chen
Let be a space-like surface immersed in a 4-dimensional pseudo-Riemannian space form with constant sectional curvature and index two. In the first part of this a…
Two optimal inequalities for anti-holomorphic submanifolds and their applications
Falleh R. Al-Solamy, Bang-Yen Chen, Sharief Deshmukh
The CR -invariant for CR-submanifolds was introduced in a recent article [B. Y. Chen, An optimal inequality for CR-warped products in complex space forms involving CR -invari…
The 2-ranks of connected compact Lie groups
Bang-Yen Chen
The 2-rank of a compact Lie group is the maximal possible rank of the elementary 2-subgroup of . The study of 2-ranks (and -ran…
-Invariants, Inequalities of Submanifolds and Their Applications
Bang-Yen Chen
The famous Nash embedding theorem was aimed for in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use…
Submanifolds of warped product manifolds }} from a -harmonic viewpoint
Bang-Yen Chen, Shihshu Walter Wei
We study -harmonic maps, -harmonic morphisms, biharmonic maps, and quasiregular mappings into submanifolds of warped product Riemannian manifolds …
Riemannian Submanifolds: A Survey
Bang-Yen Chen
Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is st…
On purely real surfaces in Kaehler surfaces and Lorentz surfaces in Lorentzian Kaehler surfaces
Bang-Yen Chen
An immersion of a manifold into an indefinite Kaehler manifold is called purely real if the almost complex structure on carri…
-invariants for Lagrangian submanifolds of complex space forms
Bang-Yen Chen, Franki Dillen
The famous Nash embedding theorem published in 1956 was aiming for the opportunity to use extrinsic help in the study of (intrinsic) Riemannian geometry, if Riemannian manifolds co…
On Wintgen ideal surfaces
Bang-Yen Chen
Wintgen proved in [P. Wintgen, Sur l'inégalité de Chen-Willmore, C. R. Acad. Sci. Paris, 288 (1979), 993--995] that the Gauss curvature and the normal curvature of a surf…