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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...

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Published in: The Journal of Geometric Analysis
ISBN: 1559-002X
ISSN: 1050-6926 1559-002X
Published: Springer 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa43216
first_indexed 2018-08-04T03:57:49Z
last_indexed 2018-11-08T20:13:19Z
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spelling 2018-11-08T17:14:08.4152099 v2 43216 2018-08-04 Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds 6734caa6d9a388bd3bd8eb0a1131d0de Feng-yu Wang Feng-yu Wang true false 2018-08-04 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. Journal Article The Journal of Geometric Analysis Springer 1559-002X 1050-6926 1559-002X 31 12 2018 2018-12-31 10.1007/s12220-018-0080-9 COLLEGE NANME COLLEGE CODE Swansea University 2018-11-08T17:14:08.4152099 2018-08-04T01:10:50.9313143 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Feng-yu Wang 1 0043216-04082018011140.pdf 17bN.pdf 2018-08-04T01:11:40.8830000 Output 344748 application/pdf Accepted Manuscript true 2019-08-27T00:00:00.0000000 true eng
title Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds
spellingShingle Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds
Feng-yu Wang
title_short Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds
title_full Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds
title_fullStr Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds
title_full_unstemmed Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds
title_sort Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds
author_id_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de
author_id_fullname_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de_***_Feng-yu Wang
author Feng-yu Wang
author2 Feng-yu Wang
format Journal article
container_title The Journal of Geometric Analysis
publishDate 2018
institution Swansea University
isbn 1559-002X
issn 1050-6926
1559-002X
doi_str_mv 10.1007/s12220-018-0080-9
publisher Springer
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2018-12-31T13:37:45Z
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score 11.048237

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