Eigenvalues of the Curvature Operator for Certain Homogeneous Manifolds
Keyword(s):
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.
1987 ◽
Vol 29
(2)
◽
pp. 245-248
◽
1994 ◽
Vol 36
(2)
◽
pp. 255-264
◽
1975 ◽
Vol 27
(3)
◽
pp. 610-617
◽
1994 ◽
Vol 36
(1)
◽
pp. 77-80
◽
2013 ◽
Vol 143
(6)
◽
pp. 1255-1289
◽
2018 ◽
Vol 97
(3)
◽
pp. 459-470
◽
1972 ◽
Vol 24
(5)
◽
pp. 799-804
◽
Keyword(s):
1953 ◽
Vol 5
◽
pp. 524-535
◽
1987 ◽
Vol 30
(2)
◽
pp. 289-293
◽