Ruy Tojeiro – författare

This book provides a comprehensive introduction to Submanifold theory, focusing on general properties of isometric and conformal immersions of Riemannian manifolds into space forms. One main theme is the isometric and conformal deformation problem for submanifolds of arbitrary dimension and codimension. Several relevant classes of submanifolds are also discussed, including constant curvature submanifolds, submanifolds of nonpositive extrinsic curvature, conformally flat submanifolds and real Kaehler submanifolds. This is the first textbook to treat a substantial proportion of the material presented here. The first chapters are suitable for an introductory course on Submanifold theory for students with a basic background on Riemannian geometry. The remaining chapters could be used in a more advanced course by students aiming at initiating research on the subject, and are also intended to serve as a reference for specialists in the field.

This contributed volume collects articles by specialists in submanifold theory, geometric analysis, and Riemannian geometry, with contributors from four continents. It is dedicated to Professor Marcos Dajczer, whose research and teaching activities have influenced new generations of geometers. Some of the works contained in this volume are written by his mathematical descendants and reflect the state of the art and current discussion in the field.Now retired from the Institute of Pure and Applied Mathematics (IMPA), Brazil, but still active, Professor Dajczer has conducted research in these and other fields, contributing to the development of submanifold theory in Brazil. He completed his undergraduate studies at the University of Buenos Aires, Argentina, in 1975, and received his PhD in Mathematics from IMPA in 1980. A postdoctoral period at the State University of New York in Stony Brook marked the beginning of a fruitful collaboration with Prof. D. Gromoll that lasted several years.Prof. Dajczer and Dr. Ruy Tojeiro are co-authors of the textbook Submanifold Theory: Beyond an Introduction, which is available in Springer's Universitext series.