Vanishing conharmonic tensor of normal locally conformal almost cosymplectic manifold

Farah H. Al-Hussaini; Aligadzhi R. Rustanov; Habeeb M. Abood

Commentationes Mathematicae Universitatis Carolinae (2020)

  • Volume: 61, Issue: 1, page 93-104
  • ISSN: 0010-2628

Abstract

top
The main purpose of the present paper is to study the geometric properties of the conharmonic curvature tensor of normal locally conformal almost cosymplectic manifolds (normal LCAC-manifold). In particular, three conhoronic invariants are distinguished with regard to the vanishing conharmonic tensor. Subsequentaly, three classes of normal LCAC-manifolds are established. Moreover, it is proved that the manifolds of these classes are η -Einstein manifolds of type ( α , β ) . Furthermore, we have determined α and β for each class.

How to cite

top

Al-Hussaini, Farah H., Rustanov, Aligadzhi R., and Abood, Habeeb M.. "Vanishing conharmonic tensor of normal locally conformal almost cosymplectic manifold." Commentationes Mathematicae Universitatis Carolinae 61.1 (2020): 93-104. <http://eudml.org/doc/297193>.

@article{Al2020,
abstract = {The main purpose of the present paper is to study the geometric properties of the conharmonic curvature tensor of normal locally conformal almost cosymplectic manifolds (normal LCAC-manifold). In particular, three conhoronic invariants are distinguished with regard to the vanishing conharmonic tensor. Subsequentaly, three classes of normal LCAC-manifolds are established. Moreover, it is proved that the manifolds of these classes are $ \eta $-Einstein manifolds of type $ (\alpha ,\beta ) $. Furthermore, we have determined $ \alpha $ and $ \beta $ for each class.},
author = {Al-Hussaini, Farah H., Rustanov, Aligadzhi R., Abood, Habeeb M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {normal locally conformal almost cosymplectic manifold; conharmonic curvature tensor; constant curvature; $ \eta $-Einstein manifold},
language = {eng},
number = {1},
pages = {93-104},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Vanishing conharmonic tensor of normal locally conformal almost cosymplectic manifold},
url = {http://eudml.org/doc/297193},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Al-Hussaini, Farah H.
AU - Rustanov, Aligadzhi R.
AU - Abood, Habeeb M.
TI - Vanishing conharmonic tensor of normal locally conformal almost cosymplectic manifold
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 1
SP - 93
EP - 104
AB - The main purpose of the present paper is to study the geometric properties of the conharmonic curvature tensor of normal locally conformal almost cosymplectic manifolds (normal LCAC-manifold). In particular, three conhoronic invariants are distinguished with regard to the vanishing conharmonic tensor. Subsequentaly, three classes of normal LCAC-manifolds are established. Moreover, it is proved that the manifolds of these classes are $ \eta $-Einstein manifolds of type $ (\alpha ,\beta ) $. Furthermore, we have determined $ \alpha $ and $ \beta $ for each class.
LA - eng
KW - normal locally conformal almost cosymplectic manifold; conharmonic curvature tensor; constant curvature; $ \eta $-Einstein manifold
UR - http://eudml.org/doc/297193
ER -

References

top
  1. Abood H. M., Al-Hussaini F. H., 10.29020/nybg.ejpam.v11i3.3261, Eur. J. Pure Appl. Math. 11 (2018), no. 3, 671–681. MR3841377DOI10.29020/nybg.ejpam.v11i3.3261
  2. Blair D. E., 10.4310/jdg/1214428097, J. Differential Geometry 1 (1967), 331–345. MR0226538DOI10.4310/jdg/1214428097
  3. Chinea D., Marrero J. C., Conformal changes of almost cosymplectic manifolds, Demonstratio Math. 25 (1992), no. 3, 641–656. MR1200763
  4. Goldberg S. I., Yano K., 10.2140/pjm.1969.31.373, Pacific J. Math. 31 (1969), 373–382. MR0251678DOI10.2140/pjm.1969.31.373
  5. Ishii Y., On conharmonic transformations, Tensor (N.S.) 7 (1957), 73–80. MR0102837
  6. Kharitonova S. V., Curvature conharmonic tensor of normal locally conformal almost cosymplectic manifolds, Vestnik OSU 12(161) (2013), 182–186. 
  7. Kirichenko V. F., Methods of generalized Hermitian geometry in the theory of almost contact manifolds, Itogi Nauki i Tekhniki, Problems of geometry 18 (1986), 25–71, 195 (Russian); translated in J. Soviet Math. 42 (1988), no. 5, 1885–1919. MR0895367
  8. Kirichenko V. F., Differential–Geometry Structures on Manifolds, Printing House, Odessa, 2013 (Russian). 
  9. Kirichenko V. F., Kharitonova S. V., On the geometry of normal locally conformal almost cosymplectic manifolds, Mat. Zametki 91 (2012), no. 1, 40–53 (Russian); translated in Math. Notes 91 (2012), no. 1–2, 34–45. MR3201391
  10. Kirichenko V. F., Rustanov A. R., Differential Geometry of quasi Sasakian manifolds, Mat. Sb. 193 (2002), no. 8, 71–100 (Russian); translated in Sb. Math. 193 (2002), no. 7–8, 1173–1201. MR1934545
  11. Olszak Z., 10.4064/cm-57-1-73-87, Colloq. Math. 57 (1989), no. 1, 73–87. MR1028604DOI10.4064/cm-57-1-73-87
  12. Olszak Z., Roça R., Normal locally conformal almost cosymplectic manifolds, Publ. Math. Debrecen 39 (1991), no. 3–4, 315–323. MR1154263
  13. Sasaki S., Hatakeyama Y., 10.2748/tmj/1178244304, Tohoku Math. J. (2) 13 (1961), 281–294. MR0138065DOI10.2748/tmj/1178244304

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.