Anti-invariant Riemannian submersions from almost Hermitian manifolds

Bayram Ṣahin

Open Mathematics (2010)

  • Volume: 8, Issue: 3, page 437-447
  • ISSN: 2391-5455

Abstract

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We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold of such submersions.

How to cite

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Bayram Ṣahin. "Anti-invariant Riemannian submersions from almost Hermitian manifolds." Open Mathematics 8.3 (2010): 437-447. <http://eudml.org/doc/269399>.

@article{BayramṢahin2010,
abstract = {We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold of such submersions.},
author = {Bayram Ṣahin},
journal = {Open Mathematics},
keywords = {Riemannian submersion; Hermitian manifold; Anti-invariant Riemannian submersion; Langrangian Riemannian submersion; anti-invariant Riemannian submersion; Kähler manifold},
language = {eng},
number = {3},
pages = {437-447},
title = {Anti-invariant Riemannian submersions from almost Hermitian manifolds},
url = {http://eudml.org/doc/269399},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Bayram Ṣahin
TI - Anti-invariant Riemannian submersions from almost Hermitian manifolds
JO - Open Mathematics
PY - 2010
VL - 8
IS - 3
SP - 437
EP - 447
AB - We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold of such submersions.
LA - eng
KW - Riemannian submersion; Hermitian manifold; Anti-invariant Riemannian submersion; Langrangian Riemannian submersion; anti-invariant Riemannian submersion; Kähler manifold
UR - http://eudml.org/doc/269399
ER -

References

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  9. [9] Marrero J.C., Rocha J., Locally conformal Khler submersions, Geom. Dedicata, 1994, 52(3), 271–289 http://dx.doi.org/10.1007/BF01278477 Zbl0810.53054
  10. [10] O’Neill B., The fundamental equations of a submersion, Mich. Math. J., 1966, 13, 458–469 
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