The conformal change of the metric of an almost Hermitian manifold applied to the antiholomorphic curvature tensor

Mileva Prvanović

Communications in Mathematics (2013)

  • Volume: 21, Issue: 1, page 77-90
  • ISSN: 1804-1388

Abstract

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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.

How to cite

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Prvanović, Mileva. "The conformal change of the metric of an almost Hermitian manifold applied to the antiholomorphic curvature tensor." Communications in Mathematics 21.1 (2013): 77-90. <http://eudml.org/doc/260630>.

@article{Prvanović2013,
abstract = {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.},
author = {Prvanović, Mileva},
journal = {Communications in Mathematics},
keywords = {almost Hermitian manifold; antiholomorphic curvature tensor; conformal change of metric; almost Hermitian manifold; antiholomorphic curvature tensor; conformal change of metric},
language = {eng},
number = {1},
pages = {77-90},
publisher = {University of Ostrava},
title = {The conformal change of the metric of an almost Hermitian manifold applied to the antiholomorphic curvature tensor},
url = {http://eudml.org/doc/260630},
volume = {21},
year = {2013},
}

TY - JOUR
AU - Prvanović, Mileva
TI - The conformal change of the metric of an almost Hermitian manifold applied to the antiholomorphic curvature tensor
JO - Communications in Mathematics
PY - 2013
PB - University of Ostrava
VL - 21
IS - 1
SP - 77
EP - 90
AB - 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.
LA - eng
KW - almost Hermitian manifold; antiholomorphic curvature tensor; conformal change of metric; almost Hermitian manifold; antiholomorphic curvature tensor; conformal change of metric
UR - http://eudml.org/doc/260630
ER -

References

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  1. Ganchev, G., Almost Hermitian manifolds similar to the complex space forms, C. R. Acad. Bulg. Sci., 32, 1979, 1179-1182, (1979) MR0562931
  2. Ganchev, G., Bochner curvature tensors in almost Hermitian manifolds, PLISKA, Stud. Math. Bulg., 9, 1987, 33-43, (1987) Zbl0622.53013MR0892678
  3. Mikeš, J., Kiosak, V., Vanžurová, A., Geodesic Mappings of Manifolds with Affine Connection, 2008, Palacký University, Faculty of Science, Olomouc, (2008) Zbl1176.53004MR2488821
  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, (1998) MR1640886
  5. Prvanović, M., Some applications of the holomorphic curvature tensor, Tensor, N.S., 66, 2005, 101-112, (2005) MR2165152
  6. Prvanović, M., 10.1007/s00022-012-0111-9, J. Geom., 103, 2012, 89-101, (2012) Zbl1259.53029MR2944551DOI10.1007/s00022-012-0111-9
  7. Tricerrri, F., Vanhecke, L., 10.1090/S0002-9947-1981-0626479-0, Trans. Amer. Math. Soc., 267, 1981, 365-398, (1981) MR0626479DOI10.1090/S0002-9947-1981-0626479-0

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