Total Mean Curvature and Submanifolds of Finite Type

During the last four decades, there were numerous important developments on total mean curvature and the theory of finite type submanifolds. This unique and expanded second edition comprises a comprehensive account of the latest updates and new results that cover total mean curvature and submanifolds of finite type. The longstanding biharmonic conjecture of the author's and the generalized biharmonic conjectures are also presented in details. This book will be of use to graduate students and researchers in the field of geometry.

Contents:

• Differentiable Manifolds
• Riemannian and Pseudo-Riemannian Manifolds
• Hodge Theory and Spectral Geometry
• Submanifolds
• Total Mean Curvature
• Submanifolds of Finite Type
• Biharmonic Submanifolds and Biharmonic Conjectures
• λ-biharmonic and Null 2-type Submanifolds
• Applications of Finite Type Theory
• Additional Topics in Finite Type Theory

Readership: Researchers and graduate students in geometry.
Key Features:

• Provides a comprehensive overview of recent developments on both theories of total mean curvature and of submanifolds of finite type
• A unique book which gives a detailed account of recent developments of the long-standing biharmonic conjecture
• Historical background is provided at the beginning of each chapter