| Title:
|
Affine connections on almost para-cosymplectic manifolds (English) |
| Author:
|
Blaga, Adara M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
863-871 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Identities for the curvature tensor of the Levi-Cività connection on an almost para-cosymplectic manifold are proved. Elements of harmonic theory for almost product structures are given and a Bochner-type formula for the leaves of the canonical foliation is established. (English) |
| Keyword:
|
para-cosymplectic manifold |
| Keyword:
|
harmonic product structure |
| MSC:
|
53C05 |
| MSC:
|
53C15 |
| MSC:
|
58A10 |
| MSC:
|
70G45 |
| idZBL:
|
Zbl 1249.53038 |
| idMR:
|
MR2853097 |
| DOI:
|
10.1007/s10587-011-0033-y |
| . |
| Date available:
|
2011-09-22T14:52:40Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141644 |
| . |
| Reference:
|
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| Reference:
|
[2] Dacko, P., Olszak, Z.: On weakly para-cosymplectic manifolds of dimension $3$.J. Geom. Phys. 57 (2007), 561-570. Zbl 1123.53015, MR 2271205, 10.1016/j.geomphys.2006.05.001 |
| Reference:
|
[3] Erdem, S.: On almost (para)contact (hyperbolic) metric manifolds and harmonicity of $(\varphi,\varphi')$-holomorphic maps between them.Houston J. Math. 28 (2002), 21-45. MR 1876938 |
| Reference:
|
[4] Funabashi, S., Kim, H. S., Kim, Y.-M., Pak, J. S.: Traceless component of the conformal curvature tensor in Kähler manifold.Czech. Math. J. 56 (2006), 857-874. Zbl 1164.53382, MR 2261658, 10.1007/s10587-006-0061-1 |
| Reference:
|
[5] Jianming, W.: Harmonic complex structures.Chin. Ann. Math., Ser. A 30 (2009), 761-764; arXiv: 1007.4392v1/math.DG (2010). MR 2650148 |
| Reference:
|
[6] Olszak, Z.: On almost cosymplectic manifolds.Kodai Math. J. 4 (1981), 239-250. Zbl 0451.53035, MR 0630244, 10.2996/kmj/1138036371 |
| Reference:
|
[7] Prvanović, M.: Holomorphically projective transformations in a locally product space.Math. Balk. 1 (1971), 195-213. MR 0288710 |
| Reference:
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[8] Schäfer, L.: $tt^*$-bundles in para-complex geometry, special para-Kähler manifolds and para-pluriharmonic maps.Differ. Geom. Appl. 24 (2006), 60-89. Zbl 1093.53046, MR 2193748, 10.1016/j.difgeo.2005.07.001 |
| Reference:
|
[9] Xin, Y. L.: Geometry of Harmonic Maps. Progress in Nonlinear Differential Equations and Their Applications 23.Birkhäuser Boston (1996). MR 1391729 |
| . |
