Journal article 1059 views 170 downloads
Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds
Feng-yu Wang
The Journal of Geometric Analysis
Swansea University Author: Feng-yu Wang
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DOI (Published version): 10.1007/s12220-018-0080-9
Abstract
We establish variational formulas for Ricci upper and lower bounds, as well as a derivative formula for the Ricci curvature. Combining these with derivative and Hessian formulas of the heat semigroup developed from stochastic analysis, we identify constant curvature manifolds, Einstein manifolds and...
| Published in: | The Journal of Geometric Analysis |
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| ISBN: | 1559-002X |
| ISSN: | 1050-6926 1559-002X |
| Published: |
Springer
2018
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa43216 |
| Abstract: |
We establish variational formulas for Ricci upper and lower bounds, as well as a derivative formula for the Ricci curvature. Combining these with derivative and Hessian formulas of the heat semigroup developed from stochastic analysis, we identify constant curvature manifolds, Einstein manifolds and Ricci parallel manifolds by using analytic formulas and semigroup inequalities.Moreover, explicit Hessian estimates are derived for the heat semigroup on Einstein and Ricci parallel manifolds. |
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| College: |
Faculty of Science and Engineering |