Submanifolds with parallel Ricci tensor (Q1110111)

From MaRDI portal





scientific article; zbMATH DE number 4071848
Language Label Description Also known as
English
Submanifolds with parallel Ricci tensor
scientific article; zbMATH DE number 4071848

    Statements

    Submanifolds with parallel Ricci tensor (English)
    0 references
    0 references
    1988
    0 references
    The author gives a classification of submanifolds of a Riemannian manifold of constant sectional curvature having parallel Ricci tensor, parallel mean curvature vector field and trivial normal connection. A corollary is the classification of 2-codimensional Einstein submanifolds of a Riemannian manifold of constant sectional curvature having parallel mean curvature vector field. It is shown that the submanifolds in question have parallel second fundamental form. The proof of Theorem 1 as it is written in the paper seems to be incomplete but the lacking arguments can be supplied rather easily.
    0 references
    parallel Ricci tensor
    0 references
    parallel mean curvature vector
    0 references
    normal connection
    0 references
    Einstein submanifolds
    0 references

    Identifiers