g -natural metrics of constant curvature on unit tangent sphere bundles

M. T. K. Abbassi; Giovanni Calvaruso

Archivum Mathematicum (2012)

  • Volume: 048, Issue: 2, page 81-95
  • ISSN: 0044-8753

Abstract

top
We completely classify Riemannian g -natural metrics of constant sectional curvature on the unit tangent sphere bundle T 1 M of a Riemannian manifold ( M , g ) . Since the base manifold M turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian g -natural metric on the unit tangent sphere bundle of a Riemannian surface.

How to cite

top

Abbassi, M. T. K., and Calvaruso, Giovanni. "$g$-natural metrics of constant curvature on unit tangent sphere bundles." Archivum Mathematicum 048.2 (2012): 81-95. <http://eudml.org/doc/246120>.

@article{Abbassi2012,
abstract = {We completely classify Riemannian $g$-natural metrics of constant sectional curvature on the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,g)$. Since the base manifold $M$ turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian $g$-natural metric on the unit tangent sphere bundle of a Riemannian surface.},
author = {Abbassi, M. T. K., Calvaruso, Giovanni},
journal = {Archivum Mathematicum},
keywords = {unit tangent sphere bundle; $g$-natural metric; curvature tensor; contact metric geometry; unit tangent sphere bundle; -natural metric; curvature tensor; contact metric geometry},
language = {eng},
number = {2},
pages = {81-95},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {$g$-natural metrics of constant curvature on unit tangent sphere bundles},
url = {http://eudml.org/doc/246120},
volume = {048},
year = {2012},
}

TY - JOUR
AU - Abbassi, M. T. K.
AU - Calvaruso, Giovanni
TI - $g$-natural metrics of constant curvature on unit tangent sphere bundles
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 2
SP - 81
EP - 95
AB - We completely classify Riemannian $g$-natural metrics of constant sectional curvature on the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,g)$. Since the base manifold $M$ turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian $g$-natural metric on the unit tangent sphere bundle of a Riemannian surface.
LA - eng
KW - unit tangent sphere bundle; $g$-natural metric; curvature tensor; contact metric geometry; unit tangent sphere bundle; -natural metric; curvature tensor; contact metric geometry
UR - http://eudml.org/doc/246120
ER -

References

top
  1. Abbassi, K. M. T., Calvaruso, G., 10.1007/s00605-006-0421-9, Monaths. Math. 151 (2006), 89–109. (2006) DOI10.1007/s00605-006-0421-9
  2. Abbassi, K. M. T., Calvaruso, G., The curvature tensor of g -natural metrics on unit tangent sphere bundles, Int. J. Contemp. Math. Sci. 6 (3) (2008), 245–258. (2008) Zbl1148.53018MR2400090
  3. Abbassi, K. M. T., Kowalski, O., 10.1016/j.difgeo.2009.05.007, Differential Geom. Appl. 28 (2010), 131–139. (2010) Zbl1190.53020MR2594457DOI10.1016/j.difgeo.2009.05.007
  4. Abbassi, K. M. T., Sarih, M., On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. (Brno) 41 (2005), 71–92. (2005) Zbl1114.53015MR2142144
  5. Abbassi, K. M. T., Sarih, M., On some hereditary properties of Riemannian g -natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl. 22 (1) (2005), 19–47. (2005) Zbl1068.53016MR2106375
  6. Boeckx, E., Vanhecke, L., 10.1023/A:1013779805244, Czechoslovak Math. J. 51 (2001), 523–544. (2001) MR1851545DOI10.1023/A:1013779805244
  7. Calvaruso, G., Contact metric geometry of the unit tangent sphere bundle. In: Complex, Contact and Symmetric manifolds, in Honor of L. Vanhecke, : Complex, Contact and Symmetric manifolds, in Honor of L. Vanhecke, Progr. Math. 234 (2005), 271–285. (2005) MR2105140
  8. Kolář, I., Michor, P. W., Slovák, J., Natural operations in differential geometry, Springer–Verlag, Berlin, 1993. (1993) Zbl0782.53013MR1202431
  9. Kowalski, O., On curvature homogeneous spaces, Publ. Dep. Geom. Topologia, Univ. Santiago Compostela (Cordero, L. A. et al., ed.), 1998, pp. 193–205. (1998) Zbl0911.53030
  10. Kowalski, O., Sekizawa, M., Natural transformations of Riemannian metrics on manifolds to metrics on tangent bundles – a classification, Bull. Tokyo Gakugei Univ. (4) 40 (1988), 1–29. (1988) Zbl0656.53021MR0974641

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.