Recent Advances in Differential Geometry and Related Areas

Bogdan D. Suceavă, Adara M. Blaga, Marian Ioan Munteanu, Cezar Oniciuc

• Publisher: American Mathematical Society
• Year: 2025
• Topic: Mathematics
• Subtopic: Mathematics General
• eBook ISBN:
  9781470480202
• Index: Mathematics

This volume contains the proceedings of the AMS Special Session on Recent Advanced in Differential Geometry, held virtually on April 1–2, 2023, and the Tenth Congress of Romanian Mathematicians Special Session on Recent Advances in the Geometry of Submanifolds, held on June 30–July 5, 2023, in Pite?ti, Romania. In the last two decades, various techniques produced new results in differential geometry and many of them focused on the geometry of submanifolds, where one of the most important questions, the Willmore conjecture, was solved in 2012 by A. Neves and F. Coda Marques. This invites a reflection on the new trends and research directions that contemporary differential geometry might and will take in its natural development. Some of the most important advances have been obtained by using techniques in geometric analysis, while others have been using more classical methods, which are still of interest. Motivated by these new developments, the present volume intends to bring together various viewpoints on the recent study of representing the fundamental idea of space in differential geometry. Of particular interest are the results focused on minimal submanifolds and their generalizations and the related concept of harmonic mappings and their generalizations. In preparing this volume, the editors were particularly interested in the study of curvature functionals in various contexts, from comparison geometry to new curvature invariants, relations between curvature and topology, as well as other related topics.

Table of contents

• Cover
• Title page
• Contents
• Preface
• Bibliography
• Harmonicity and biharmonicity of quadratic maps between spheres
• A survey on submanifolds of nearly Kähler spaces
• Expressions of circles in a complex hyperbolic space by trajectories on tubes around complex hyperplanes
• On conservation laws for polyharmonic maps
• Chen inequality for statistical submanifolds in Kenmotsu statistical manifolds of constant 𝜙-sectional curvature
• Thurston geometries in dimension four from a Riemannian perspective
• Recent results in Ricci and Yamabe solitons in contact geometry
• Understanding of constant 𝑝-mean curvature hypersurfaces in the Heisenberg groups
• Open problems on compact constant mean curvature surfaces with boundary
• On holomorphic conformal structures associated with lattice polarized K3 surfaces
• Triharmonic curves in the 3-dimensional Sol space
• A note on Weingarten surfaces foliated by helices
• Characterizations of rotational biconservative hypersurfaces
• Einstein warped-product manifolds and the screened Poisson equation
• Back Cover