| Title:
|
On applications of the Yano–Ako operator (English) |
| Author:
|
Magden, A. |
| Author:
|
Salimov, A. A. |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
135-141 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider a method by which a skew-symmetric tensor field of type (1,2) in $M_{n}$ can be extended to the tensor bundle $T_q^0(M_n)$ $(q>0)$ on the \textit{pure cross-section.} The results obtained are to some extend similar to results previously established for cotangent bundles $T_{1}^{0}(M_{n})$. However, there are various important differences and it appears that the problem of lifting tensor fields of type (1,2) to the tensor bundle $T_{q}^{0}(M_{n})$ $(q>1)$ on the \textit{pure cross-section} presents difficulties which are not encountered in the case of the cotangent bundle. (English) |
| Keyword:
|
Lift |
| Keyword:
|
tensor bundle |
| Keyword:
|
pure tensor |
| Keyword:
|
operator Yano--Ako |
| MSC:
|
53A45 |
| MSC:
|
53C05 |
| MSC:
|
53C15 |
| MSC:
|
53C25 |
| MSC:
|
53C55 |
| idZBL:
|
Zbl 1129.53015 |
| idMR:
|
MR2321305 |
| . |
| Date available:
|
2009-08-21T07:05:31Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133446 |
| . |
| Reference:
|
[1] Ledger A., Yano K.: Almost complex structures on tensor bundles.J. Dif. Geom. 1 (1967), 355–368. Zbl 0157.28402, MR 0226560 |
| Reference:
|
[2] Salimov A. A., Magden A.: Complete lifts of tensor fields on a pure cross-section in the tensor bundle $T_{q}^{1}(M_{n})$.Note di Matematica 18, 1 (1998), 27–37. MR 1759013 |
| Reference:
|
[3] Cengiz N., Salimov A. A.: Complete lifts of derivations to tensor bundles.Bol. Soc. Mat. Mexicana (3) 8, 1 (2002), 75–82. Zbl 1020.53006, MR 1916892 |
| Reference:
|
[4] Yano K., Ako M.: On certain operators associated with tensor fields.Kodai Math. Sem. Rep. 20 (1968), 414–436. Zbl 0167.19702, MR 0234370 |
| Reference:
|
[5] Salimov A. A.: Generalized Yano–Ako operator and the complete lift of tensor fields.Tensor N. S., Tensor Soc. of Japan 55, 2 (1994), 142–146. Zbl 0818.53032, MR 1310107 |
| Reference:
|
[6] Cengiz N., Salimov A. A.: Diagonal lift in the tensor bundle and its applications.Appl. Math. Comput. 142, 2–3 (2003), 309–319. Zbl 1034.53016, MR 1979438 |
| Reference:
|
[7] Salimov A. A., Cengiz N.: Lift of Riemannian metrics to tensor bundles.Russian Math. (IZ. VUZ) 47, 11 (2003), 47–55. MR 2038854 |
| Reference:
|
[8] Magden A., Cengiz N., Salimov A. A.: Horizontal lift of affinor structures and its applications.Appl. Math. Comput. 156, 2 (2004), 455–461. Zbl 1073.53044, MR 2087522 |
| . |
