The nonexistence of rank 4 IP tensors in signature (1,3)
Let V be a real vector space of dimension 4 with a nondegenerate symmetric bilinear form of signature (1,3). We show that there exists no algebraic curvature tensor R on V so that its associated skew-symmetric operator R(⋅) has rank 4 and constant eigenvalues on the Grassmannian of nondegenerate 2-p...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202108106 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559952124706816 |
|---|---|
| author | Kelly Jeanne Pearson Tan Zhang |
| author_facet | Kelly Jeanne Pearson Tan Zhang |
| author_sort | Kelly Jeanne Pearson |
| collection | DOAJ |
| description | Let V be a real vector space of dimension 4 with a nondegenerate symmetric bilinear form of signature (1,3). We show that there exists no algebraic curvature tensor R on V so that its associated skew-symmetric operator R(⋅) has rank 4 and constant eigenvalues on the Grassmannian of nondegenerate 2-planes in V. |
| format | Article |
| id | doaj-art-16d09467182b4e5c9824a42f845a08f4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-16d09467182b4e5c9824a42f845a08f42025-02-03T01:28:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0131525926910.1155/S0161171202108106The nonexistence of rank 4 IP tensors in signature (1,3)Kelly Jeanne Pearson0Tan Zhang1Department of Mathematics and Statistics, Murray State University, Murray 42071-0009, KY, USADepartment of Mathematics and Statistics, Murray State University, Murray 42071-0009, KY, USALet V be a real vector space of dimension 4 with a nondegenerate symmetric bilinear form of signature (1,3). We show that there exists no algebraic curvature tensor R on V so that its associated skew-symmetric operator R(⋅) has rank 4 and constant eigenvalues on the Grassmannian of nondegenerate 2-planes in V.http://dx.doi.org/10.1155/S0161171202108106 |
| spellingShingle | Kelly Jeanne Pearson Tan Zhang The nonexistence of rank 4 IP tensors in signature (1,3) International Journal of Mathematics and Mathematical Sciences |
| title | The nonexistence of rank 4 IP tensors in signature (1,3) |
| title_full | The nonexistence of rank 4 IP tensors in signature (1,3) |
| title_fullStr | The nonexistence of rank 4 IP tensors in signature (1,3) |
| title_full_unstemmed | The nonexistence of rank 4 IP tensors in signature (1,3) |
| title_short | The nonexistence of rank 4 IP tensors in signature (1,3) |
| title_sort | nonexistence of rank 4 ip tensors in signature 1 3 |
| url | http://dx.doi.org/10.1155/S0161171202108106 |
| work_keys_str_mv | AT kellyjeannepearson thenonexistenceofrank4iptensorsinsignature13 AT tanzhang thenonexistenceofrank4iptensorsinsignature13 AT kellyjeannepearson nonexistenceofrank4iptensorsinsignature13 AT tanzhang nonexistenceofrank4iptensorsinsignature13 |