Semiparallel Submanifolds in Space Forms

This book offers the most comprehensive survey to date of the theory of semiparallel submanifolds. It begins with the necessary background material, detailing symmetric and semisymmetric Riemannian manifolds, smooth manifolds in space forms, and parallel submanifolds. The book then introduces semiparallel submanifolds and gives some characterizations for their class and several subclasses. Coverage next discusses the concept of main symmetric orbit and presents all known results concerning umbilic-like main symmetric orbits. Presenting both background material and the most recent developments in semiparallel submanifolds, this book will appeal to both researchers and graduate students.

Author has published more than 40 papers in the field, so readers are assured of an authoritative treatment Covers both necessary background and cutting edge research in the field Goes beyond common examples, such as Euclidean space, to consider the examples of Segre, Plucker, and Veronese

Auteur

Ülo Lumiste is considered an expert in the application of Cartan's exterior calculus. He has been noted for his extensive contributions to the area of semiparallel submanifolds.

Texte du rabat

This book offers a comprehensive survey to date of the theory of semiparallel submanifolds. Introduced in 1985, semiparallel submanifolds have emerged as an important area of research within differential geometry and topology.

The author begins with the necessary background on symmetric and semisymmetric Riemannian manifolds, smooth manifolds in space forms, and parallel submanifolds. Semiparallel submanifolds are introduced in Chapter 4, where characterizations of their class and several subclasses are given. In later chapters Lumiste introduces the concept of main symmetric orbit and presents all known results concerning umbilic-like main symmetric orbits. Generalizations, such as k-semiparallel submanifolds and Ric-semiparallel hypersurfaces, are also studied.

Semiparallel Submanifolds in Space Forms will appeal to both researchers and graduate students.

Contenu
Preliminaries.- Submanifolds in Space Forms.- Parallel Submanifolds.- Semiparallel Submanifolds.- Normally Flat Semiparallel Submanifolds.- Semiparallel Surfaces.- Semiparallel Three-Dimensional Submanifolds.- Decomposition Theorems.- Umbilic-Likeness of Main Symmetric Orbits.- Geometric Descriptions in General.- Isometric Semiparallel Immersions of Riemannian Manifolds of Conullity Two.- Some Generalizations.