Characterizations of Trivial Ricci Solitons
Finding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton. First, on a complete shrinking Ricci soliton, we show that the scalar curvature satisfying a certain inequality gives a ch...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/9826570 |
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| Summary: | Finding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton. First, on a complete shrinking Ricci soliton, we show that the scalar curvature satisfying a certain inequality gives a characterization of a trivial Ricci soliton. Then, it is shown that the potential field having geodesic flow and length of potential field satisfying certain inequality gives another characterization of a trivial Ricci soliton. Finally, we show that the potential field of constant length satisfying an inequality gives a characterization of a trivial Ricci soliton. |
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| ISSN: | 1687-9120 1687-9139 |