The purpose of this book is to introduce the reader to two interesting topics in geometry which have developed over the last fifteen years, namely, total mean curvature and submanifolds of finite type. The theory of total mean curvature is the study of the integral of the n-th power of the mean curvature of a compact n-dimensional submanifold in a Euclidean m-space and its applications to other branches of mathematics. The relation of total mean curvature to analysis, geometry and topology are discussed in detail. Motivated from these studies, the author introduces and studies submanifolds of...
The purpose of this book is to introduce the reader to two interesting topics in geometry which have developed over the last fifteen years, namely, to...
Provides an introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. In this book, a number of results on pseudo-Riemannian submanifolds are also included.
Provides an introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming fro...
During the last four decades, there were numerous important developments on total mean curvature and the theory of finite type submanifolds. This book presents a comprehensive account of the latest updates and new results that cover total mean curvature, submanifolds of finite type as well as on the long-standing biharmonic conjecture of the author's and the generalized biharmonic conjectures.
During the last four decades, there were numerous important developments on total mean curvature and the theory of finite type submanifolds. This book...
