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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Conformally Deformable Hypersurfaces,vial conformal deformations. Besides conformally flat hypersurfaces, the simplest examples are those that are conformally congruent to cylinders and rotation hypersurfaces over surfaces in ., and to cylinders over three-dimensional hypersurfaces of . that are cones over surfaces in .. These examples are called .hypersurfaces.

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整顿

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Submanifolds with Nonpositive Extrinsic Curvature,curvature must be positive. It turns out that the simple idea in the proof of this elementary fact has far-reaching generalizations for non-necessarily compact submanifolds in fairly general ambient Riemannian manifolds.

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Reduction of Codimension,. < . means that there exists a totally geodesic submanifold . in . such that .. The possibility of reducing the codimension fits into the fundamental problem of determining the least possible codimension of an isometric immersion of a given Riemannian manifold into a space of constant sectional curvature.

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Isometric Immersions of Riemannian Products,rics 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 tangent spaces to each factor are preserved by all shape operators.

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Genuine Deformations, studying the isometric deformations of a submanifold, one should look for the “genuine” ones, that is, those which are not induced by isometric deformations of an “extended” submanifold of higher dimension. Besides, it is also of interest to consider isometric deformations of a submanifold that take place in a possibly different codimension.

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0172-5939 ier of knowledge in the subject?.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