Abstract
In this paper, we classify three-dimensional Lorentzian Lie groups on which Ricci tensors associated with Bott connections, canonical connections and Kobayashi–Nomizu connections are Codazzi tensors associated with these connections. We also classify three-dimensional Lorentzian Lie groups with the quasi-statistical structure associated with Bott connections, canonical connections and Kobayashi–Nomizu connections.
Highlights
In [1], Andrzej and Shen studied some geometric and topological consequences of the existence of a non-trivial Codazzi tensor on a Riemannian manifold
Our research shows that the Ricci tensors of Bott connections, canonical connections and Kobayashi–Nomizu connections are Codazzi tensors can be used as an affine parallel to the above results in [10]
We classify threedimensional Lorentzian Lie groups with the quasi-statistical structure associated with Bott connections, canonical connections and Kobayashi–Nomizu connections
Summary
In [1], Andrzej and Shen studied some geometric and topological consequences of the existence of a non-trivial Codazzi tensor on a Riemannian manifold. In [1], Andrzej and Shen showed that the existence of nontrivial Codazzi tensors on Riemannian manifolds induces some geometric and topological results. We classify threedimensional Lorentzian Lie groups with the quasi-statistical structure associated with Bott connections, canonical connections and Kobayashi–Nomizu connections.
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