Submanifold Theory Beyond an Introduction /

• Main Authors: Dajczer, Marcos (Author, http://id.loc.gov/vocabulary/relators/aut), Tojeiro, Ruy (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer US : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Universitext,
• Subjects: Manifolds (Mathematics).; Complex manifolds.; Differential geometry.; Algebra.; Manifolds and Cell Complexes (incl. Diff.Topology).; Differential Geometry.; General Algebraic Systems.

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 codimens...

Table of Contents:

• The basic equations of a submanifold
• Reduction of codimension
• Minimal submanifolds
• Local rigidity of submanifolds
• Constant curvature submanifolds
• Submanifolds with nonpositive extrinsic curvature
• Submanifolds with relative nullity
• Isometric immersions of Riemannian products
• Conformal immersions
• Isometric immersions of warped products
• The Sbrana-Cartan hypersurfaces
• Genuine deformations
• Deformations of complete submanifolds
• Innitesimal bendings
• Real Kaehler submanifolds
• Conformally at submanifolds
• Conformally deformable hypersurfaces
• Vector bundles. .