219 citations
- East China Normal UniversityCN4 papers
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- University of KentuckyUS3 papers
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7 papers · 1 filter
Manifolds with commuting Jacobi operators
M. Brozos-Vazquez, P. Gilkey
We characterize Riemannian manifolds of constant sectional curvature in terms of commutation properties of their Jacobi operators.
A note on uniformization of Riemann surfaces by Ricci flow
Xiuxiong Chen, Peng Lu, Gang Tian
In this note we clarify that the Rcci flow can be used to give an independent proof of the uniformization theorem of Riemann surfaces.
Affine curvature homogeneous 3-dimensional Lorentz Manifolds
P. Gilkey, S. Nikcevic
We study a family of 3-dimensional Lorentz manifolds. Some members of the family are 0-curvature homogeneous, 1-affine curvature homogeneous, but not 1-curvature homogeneous. Some…
Eigenforms of the Laplacian for Riemannian V-submersions
Peter B. Gilkey, Hong-Jong Kim, JeongHyeong Park
Let p: Z -> Y be a Riemannian V-submersion of compact V-manifolds. We study when the pull-back of an eigenform of the Laplacian on Y is an eigenform of the Laplacian on Z, and when…
Manifolds which are Ivanov-Petrova or k-Stanilov
P. Gilkey, S. Nikcevic, V. Videv
We present some examples of curvature homogeneous pseudo-Riemannian manifolds which are k-spacelike Jordan Stanilov; their higher order curvature operator has constant Jordan norma…
Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2
Peter Gilkey, Tan Zhang
Let R be an algebraic curvature tensor for a non-degenerate inner product of signature(p,q) where q>4. If is a spacelike 2 plane, let be the associated skew-symmetric cu…