Geometric Properties of Natural Operator

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A central problem in differential geometry is to relate algebraic properties of the Riemann curvature tensor to the underlying geometry of the manifold. The full curvature tensor is in general quite difficult to deal with. This book presents results…

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    Om Geometric Properties of Natural Operator

    A central problem in differential geometry is to relate algebraic properties of the Riemann curvature tensor to the underlying geometry of the manifold. The full curvature tensor is in general quite difficult to deal with. This book presents results about the geometric consequences that follow if various natural operators defined in terms of the Riemann curvature tensor (the Jacobi operator, the skew-symmetric curvature operator, the Szabo operator, and higher order generalizations) are assumed to have constant eigenvalues or constant Jordan normal form in the appropriate domains of definition.The book presents algebraic preliminaries and various Schur type problems; deals with the skew-symmetric curvature operator in the real and complex settings and provides the classification of algebraic curvature tensors whose skew-symmetric curvature has constant rank 2 and constant eigenvalues; discusses the Jacobi operator and a higher order generalization and gives a unified treatment of the Osserman conjecture and related questions; and establishes the results from algebraic topology that are necessary for controlling the eigenvalue structures. An extensive bibliography is provided. Results are described in the Riemannian, Lorentzian, and higher signature settings, and many families of examples are displayed.Contents:Algebraic Curvature TensorsThe Skew-Symmetric Curvature OperatorThe Jacobi OperatorControlling the Eigenvalue StructureReadership: Researchers and graduate students in geometry and topology.Key Features: These are no competing titlesProminents authors from all over the world cover the most exciting fields of particle physics and cosmology, both theoretically and experimentallyHighly valuable as textbook for students

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    Detaljer

    Format
    E-Bok
    Filformat
    PDF
    Utgivelsesår
    2001
    Forlag
    World Scientific Publishing Co
    Språk
    Engelsk
    ISBN
    9789812799692
    Sider
    316

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