Journal article 942 views 153 downloads
Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds
The Journal of Geometric Analysis
Swansea University Author:
Feng-yu Wang
-
PDF | Accepted Manuscript
Download (363.77KB)
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 |
---|---|
ISBN: | 1559-002X |
ISSN: | 1050-6926 1559-002X |
Published: |
Springer
2018
|
Online Access: |
Check full text
|
URI: | https://cronfa.swan.ac.uk/Record/cronfa43216 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
first_indexed |
2018-08-04T03:57:49Z |
---|---|
last_indexed |
2018-11-08T20:13:19Z |
id |
cronfa43216 |
recordtype |
SURis |
fullrecord |
<?xml version="1.0"?><rfc1807><datestamp>2018-11-08T17:14:08.4152099</datestamp><bib-version>v2</bib-version><id>43216</id><entry>2018-08-04</entry><title>Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds</title><swanseaauthors><author><sid>6734caa6d9a388bd3bd8eb0a1131d0de</sid><ORCID>0000-0003-0950-1672</ORCID><firstname>Feng-yu</firstname><surname>Wang</surname><name>Feng-yu Wang</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2018-08-04</date><deptcode>SMA</deptcode><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.</abstract><type>Journal Article</type><journal>The Journal of Geometric Analysis</journal><publisher>Springer</publisher><isbnElectronic>1559-002X</isbnElectronic><issnPrint>1050-6926</issnPrint><issnElectronic>1559-002X</issnElectronic><keywords/><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2018</publishedYear><publishedDate>2018-12-31</publishedDate><doi>10.1007/s12220-018-0080-9</doi><url/><notes/><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SMA</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2018-11-08T17:14:08.4152099</lastEdited><Created>2018-08-04T01:10:50.9313143</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Feng-yu</firstname><surname>Wang</surname><orcid>0000-0003-0950-1672</orcid><order>1</order></author></authors><documents><document><filename>0043216-04082018011140.pdf</filename><originalFilename>17bN.pdf</originalFilename><uploaded>2018-08-04T01:11:40.8830000</uploaded><type>Output</type><contentLength>344748</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2019-08-27T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807> |
spelling |
2018-11-08T17:14:08.4152099 v2 43216 2018-08-04 Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds 6734caa6d9a388bd3bd8eb0a1131d0de 0000-0003-0950-1672 Feng-yu Wang Feng-yu Wang true false 2018-08-04 SMA 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 Mathematics COLLEGE CODE SMA 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 0000-0003-0950-1672 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 |
2018-12-31T03:54:28Z |
_version_ |
1763752719408955392 |
score |
11.021648 |