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Eigenvalues of the Curvature Operator for Certain Homogeneous Manifolds

Published online by Cambridge University Press:  20 November 2018

J. E. D'Atri  and
I. Dotti Miatello
J. E. D'Atri
Affiliation:
Mathematics Department, Rutgers University, New Brunswick, N.J. 08903, USA
I. Dotti Miatello
Affiliation:
FAMAF, Universidad Nacional de Córdoba, Valparaiso y Rogelio Martinez, 5032 Cordoba, Argentina
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Given a Riemannian manifold M, the Riemann tensor R induces the curvature operator on the exterior power of the tangent space, defined by the formula where the inner product is defined by From the symmetries of R, it follows that ρ is self-adjoint and so has only real eigenvalues. R also induces the sectional curvature function K on 2-planes in is an orthonormal basis of the 2-plane π.

Keywords

53C20 53C30
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 6 , 01 December 1990 , pp. 981 - 999
Copyright
Copyright © Canadian Mathematical Society 1990

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