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arXiv · 2205.00332

Geometry in the large on Hadamard manifolds

Sergey Stepanov·Irina Tsyganok
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Abstract

In this paper, we prove several Liouville-type theorems on the non-existence of Killing-Yano tensors, Killing tensors, and harmonic symmetric tensors on Hadamard manifolds and, in particular, on Riemannian symmetric spaces of non-compact type. These theorems supplement the well-known vanishing theorems for the above tensors, obtained using the Bochner technique for compact Riemannian manifolds. In turn, the proofs of our theorems will use well-known Liouville-type theorems on the non-existence of subharmonic and harmonic functions on complete Riemannian manifolds, which we have partially modified for the case of Hadamard manifolds and, in particular, Riemannian symmetric spaces of noncompact type.

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Sergey Stepanov, Irina Tsyganok. 2022-04-30. Geometry in the large on Hadamard manifolds. https://arxiv.org/abs/2205.00332

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