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This work presents results about the geometric consequences that follow if various natural operators defined in terms of the Riemann curvature tensor are assumed to have constant eigenvalues or constant Jordan normal form in the appropriate domains of definition.

Geometry, Riemannian. --- Curvature. --- Operator theory. --- Functional analysis --- Calculus --- Curves --- Surfaces --- Riemann geometry --- Riemannian geometry --- Generalized spaces --- Geometry, Non-Euclidean --- Semi-Riemannian geometry

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Differential equations --- Riemannian manifolds. --- Spectral geometry. --- Asymptotic theory.

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Curvature --- Geometry, Riemannian --- Operator theory

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517.95 --- 517.95 Partial differential equations --- Partial differential equations --- Mathematical physics

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A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing ont

Curvature. --- Geometry. --- Mathematics --- Euclid's Elements --- Calculus --- Curves --- Surfaces