Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor is popular PDF and ePub book, written by Peter B. Gilkey in 2001, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor can be Read Online from any device for your convenience.
Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor Book PDF Summary
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 Tensors; The Skew-Symmetric Curvature Operator; The Jacobi Operator; Controlling the Eigenvalue Structure. Readership: Researchers and graduate students in geometry and topology.
Detail Book of Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor PDF
- Author : Peter B. Gilkey
- Release : 01 October 2024
- Publisher : World Scientific
- ISBN : 9789812799692
- Genre : Mathematics
- Total Page : 316 pages
- Language : English
- PDF File Size : 16,7 Mb
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