A special class of symmetric Killing 2-tensors
arXiv:1804.10149 · doi:10.1016/j.geomphys.2018.12.009
Abstract
We study symmetric Killing 2-tensors on Riemannian manifolds and show that several additional conditions can be realised only for Sasakian manifolds and Euclidean spheres. In particular we show that (three)-Sasakian manifolds can also be characterized by properties of the symmetric products of their characteristic 1-forms. Moreover, we recover a result of S.~Gallot on the characterization of spheres by means of functions satisfying a certain differential equation of order three.
arXiv comment29 pages
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