A special class of symmetric Killing 2-tensors
Differential Geometry
2019-02-20 v1
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.
Keywords
Cite
@article{arxiv.1804.10149,
title = {A special class of symmetric Killing 2-tensors},
author = {Konstantin Heil and Tillmann Jentsch},
journal= {arXiv preprint arXiv:1804.10149},
year = {2019}
}
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29 pages