| Title:
|
Particular trace decompositions and applications of trace decomposition to almost projective invariants (English) |
| Author:
|
Crâşmăreanu, Mircea |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
631-637 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
First, by using the formulae of Krupka, the trace decomposition for some particular classes of tensors of types (1, 2) and (1, 3) is obtained. Second, it is proved that the traceless part of a tensor is an almost projective invariant of weight 1. We apply this result to Weyl curvature tensors. (English) |
| Keyword:
|
traceless tensor |
| Keyword:
|
trace decomposition |
| Keyword:
|
almost projective invariant |
| MSC:
|
15A72 |
| MSC:
|
53A55 |
| idZBL:
|
Zbl 0982.15038 |
| idMR:
|
MR1970265 |
| DOI:
|
10.21136/MB.2001.134205 |
| . |
| Date available:
|
2009-09-24T21:55:09Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134205 |
| . |
| Reference:
|
[1] Codău, N.: Almost projective invariants for a (M, A)-manifold.Proceedings of Romanian Conference of Geometry and Topology, Târgovişte, 1986, Univ. Bucureşti, 1988. (Romanian) MR 0979993 |
| Reference:
|
[2] Krupka, D.: The trace decomposition of tensors of type (1, 2) and (1, 3).New Developments in Differential Geometry (Debrecen, 1994), Math. Appl., 350, Kluwer Academic Publ., Dordrecht, 1996, 243–253. Zbl 0840.15024, MR 1377288 |
| Reference:
|
[3] Krupka, D.: The trace decomposition problem.Beiträge Algebra Geom. 36 (1995), 303–315. Zbl 0839.15024, MR 1358429 |
| Reference:
|
[4] Mikeš, J.: On the general trace decomposition problem.Proc. Conf., Aug. 28–Sept. 1, 1995 Brno, Czech Republic, Masaryk Univ., Brno, 1996, pp. 45–50. MR 1406322 |
| Reference:
|
[5] Lakomá, L., Mikeš, J.: On the special trace decomposition problem on quaternion structure.Proceedings of the Third International Workshop on Differential Geometry and Its Applications and the First German-Romanian Seminar on Geometry (Sibiu, 1997), Gen. Math. 5 (1997), 225–230. MR 1723612 |
| Reference:
|
[6] Vrânceanu, Gh.: Leçons de Géométrie Différentielle, vol. I.Ed. Academiei, Bucarest, 1957. MR 0124823 |
| Reference:
|
[7] Vrânceanu, Gh.: Leçons de Géométrie Différentielle, vol. III.Ed. Academiei, Bucarest and Gauthier-Villars, Paris, 1964. MR 0124823 |
| . |
