Titlebook: Submanifold Theory; Beyond an Introducti Marcos Dajczer,Ruy Tojeiro Textbook 2019 Springer Science+Business Media, LLC, part of Springer Na

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Textbook 2019nian 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 cu

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The Basic Equations of a Submanifold,ndamental form and normal connection of an isometric immersion by means of the Gauss and Weingarten formulas. Then we derive their compatibility conditions, namely, the Gauss, Codazzi and Ricci equations. The main result of the chapter is the Fundamental theorem of submanifolds, which asserts that t

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Reduction of Codimension,er the codimension of an isometric immersion into a space of constant sectional curvature can be reduced. That an isometric immersion . admits a . to . < . means that there exists a totally geodesic submanifold . in . such that .. The possibility of reducing the codimension fits into the fundamental

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Constant Curvature Submanifolds,orms. However, the initial motivation of Cartan’s theory of exteriorly orthogonal quadratic forms, which are equivalent to symmetric flat bilinear forms with respect to positive definite inner products, was to study isometric immersions .. Indeed, the second fundamental form of such an isometric imm

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Isometric Immersions of Riemannian Products,concept discussed in this chapter. The metric induced on a product manifold by an extrinsic product of immersions is the Riemannian product of the metrics induced by the immersions of the factors, and its second fundamental form is adapted to the product net of the manifold in the sense that the tan

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