| Title:
|
The conformal change of the metric of an almost Hermitian manifold applied to the antiholomorphic curvature tensor (English) |
| Author:
|
Prvanović, Mileva |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
21 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
77-90 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By using the technique of decomposition of a Hermitian vector space under the action of a unitary group, Ganchev [2] obtained a tensor which he named the Weyl component of the antiholomorphic curvature tensor. We show that the same tensor can be obtained by direct application of the conformal change of the metric to the antiholomorphic curvature tensor. Also, we find some other conformally curvature tensors and examine some relations between them. (English) |
| Keyword:
|
almost Hermitian manifold |
| Keyword:
|
antiholomorphic curvature tensor |
| Keyword:
|
conformal change of metric |
| MSC:
|
53C56 |
| idZBL:
|
Zbl 06202725 |
| idMR:
|
MR3067122 |
| . |
| Date available:
|
2013-07-18T15:27:20Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143349 |
| . |
| Reference:
|
[1] Ganchev, G.: Almost Hermitian manifolds similar to the complex space forms.C. R. Acad. Bulg. Sci., 32, 1979, 1179-1182, MR 0562931 |
| Reference:
|
[2] Ganchev, G.: Bochner curvature tensors in almost Hermitian manifolds.PLISKA, Stud. Math. Bulg., 9, 1987, 33-43, Zbl 0622.53013, MR 0892678 |
| Reference:
|
[3] Mikeš, J., Kiosak, V., Vanžurová, A.: Geodesic Mappings of Manifolds with Affine Connection.2008, Palacký University, Faculty of Science, Olomouc, Zbl 1176.53004, MR 2488821 |
| Reference:
|
[4] Prvanović, M.: On the cutvature tensor of Kähler type in an almost Hermitian and almost anti-Hermitian manifolds.Mat. Vasnik, 50, 1998, 57-64, MR 1640886 |
| Reference:
|
[5] Prvanović, M.: Some applications of the holomorphic curvature tensor.Tensor, N.S., 66, 2005, 101-112, MR 2165152 |
| Reference:
|
[6] Prvanović, M.: Conformally invariant tensors of an almost Hermitian manifold associated with the holomorphic curvature tensor.J. Geom., 103, 2012, 89-101, Zbl 1259.53029, MR 2944551, 10.1007/s00022-012-0111-9 |
| Reference:
|
[7] Tricerrri, F., Vanhecke, L.: Curvature tensors on almost Hermitian manifolds.Trans. Amer. Math. Soc., 267, 1981, 365-398, MR 0626479, 10.1090/S0002-9947-1981-0626479-0 |
| . |
