Biharmonic Riemannian submersions from a 3-dimensional BCV space
| Autor: | Wang, Ze-Ping, Ou, Ye-Lin |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | BCV spaces are a family of 3-dimensional Riemannian manifolds which include six of Thurston's eight geometries. In this paper, we give a complete classification of proper biharmonic Riemannian submersions from a 3-dimensional BCV space by proving that such biharmonic maps exist only in the cases of $H^2\times R\to R^2$, or $\widetilde{SL}(2,R)\to R^2$. In each of these two cases, we are able to construct a family of infinitely many proper biharmonic Riemannian submersions. Our results on one hand, extend the results in [25] where a complete classification of proper biharmonic Riemannian submersions from a $3$-dimensional space form was obtained, and other other hand, can be viewed as the dual study of biharmonic surfaces (i.e., biharmonic isometric immersions) in a BCV space studied in [5, 6, 23, 14]. Comment: 25 pages |
| Databáze: | arXiv |
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