Geometry of Submanifolds

ISBN-13: 9781470450922

Joeri Van der Veken;Alfonso Carriazo;Ivko Dimitric

Opis

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.

Spis treści

• 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 $\mathbb^7$
• 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.