Geometry of Submanifolds
Published on 30. January 2021
Book
Paperback/Softback
269 pages
978-1-4704-5092-2 (ISBN)
Description
This volume contains the proceedings of the AMS Special Session on Geometry of Submanifolds, in honor or Bang-Yen Chen's 75th birthday, held from October 20-21, 2018, at the University of Michigan, Ann Arbor, Michigan. The development of contemporary geometry of submanifolds benefited greatly from Bang-Yen Chen's contributions, as several interesting questions actively pursued today originate in his work. Chen is known for several fundamental ideas in differential geometry, including Chen inequalities, Chen invariants, Chen's conjectures, Chen surface, Chen-Ricci inequality, Chen submanifolds, Chen equality, submanifolds of finite type, and slant submanifolds. The papers in this volume represent a celebration of the geometry of submanifolds and its connections with other areas of mathematics and cover themes rooted in Chen's work, from investigations on the spectrum of the Laplacian on complete Riemannian manifolds to the geometry of symmetric spaces. These contributions are written with the hope to inform and inspire.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Weight
515 gr
ISBN-13
978-1-4704-5092-2 (9781470450922)
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Schweitzer Classification
Content
Reflections on some research work of Bang-Yen Chen
My education in differential geometry and my indebtedness
Submanifold theory--A contemplation of submanifolds
Spectral gaps on complete Riemannian manifolds
On stability and index of minimal submanifolds
Maximally-warped metrics with harmonic curvature
CR-submanifolds of Chen-type two in non-flat complex space forms
On certain contact $CR$-submanifolds in $\mathbb{S}^7$
A class of strictly convex hypersurfaces satisfying Weingarten-type inequalities, I
Bounding the invariant spectrum when the scalar curvature is non-negative
Isometric immersions of surfaces: Classical approaches and integrability
On the geometry of Einstein spaces: A note on their curvature symmetries
Statistical manifolds and their submanifolds. Results on Chen-like invariants
Warped product hypersurfaces in pseudo-Riemannian real space forms
The development of rectifying submanifolds
Some recent work on biharmonic conformal maps
On isoparametric linear Weingarten hypersurfaces in Riemannian and Lorentzian space forms
Lagrangian submanifolds of the nearly Kahler 6-sphere and Chen's equality
Sesquilinear forms and symmetric spaces
Lagrangian submanifolds of the complex quadric as Gauss maps of hypersurfaces of spheres
Growth estimates for generalized harmonic forms on noncompact manifolds with geometric applications.
My education in differential geometry and my indebtedness
Submanifold theory--A contemplation of submanifolds
Spectral gaps on complete Riemannian manifolds
On stability and index of minimal submanifolds
Maximally-warped metrics with harmonic curvature
CR-submanifolds of Chen-type two in non-flat complex space forms
On certain contact $CR$-submanifolds in $\mathbb{S}^7$
A class of strictly convex hypersurfaces satisfying Weingarten-type inequalities, I
Bounding the invariant spectrum when the scalar curvature is non-negative
Isometric immersions of surfaces: Classical approaches and integrability
On the geometry of Einstein spaces: A note on their curvature symmetries
Statistical manifolds and their submanifolds. Results on Chen-like invariants
Warped product hypersurfaces in pseudo-Riemannian real space forms
The development of rectifying submanifolds
Some recent work on biharmonic conformal maps
On isoparametric linear Weingarten hypersurfaces in Riemannian and Lorentzian space forms
Lagrangian submanifolds of the nearly Kahler 6-sphere and Chen's equality
Sesquilinear forms and symmetric spaces
Lagrangian submanifolds of the complex quadric as Gauss maps of hypersurfaces of spheres
Growth estimates for generalized harmonic forms on noncompact manifolds with geometric applications.