previous :: next
Some Relationships between the Geometry of the Tangent Bundle and the Geometry of the Riemannian Base Manifold
Guillermo HENRY and Guillermo KEILHAUER
Source: Tokyo J. of Math. Volume 35, Number 1
(2012), 1-15.
Abstract
We compute the curvature tensor of the tangent bundle of a Riemannian manifold endowed with a natural metric and we get some relationships between the geometry of the base manifold and the geometry of the tangent bundle.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.tjm/1342701340
Digital Object Identifier: doi:10.3836/tjm/1342701340
Zentralblatt MATH identifier: 06073757
Mathematical Reviews number (MathSciNet): MR2977441
References
Abbassi, M. T. and Sarih, M., On some hereditary properties of Riemannian $g$-natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl. 22 (2005), 1: 19–47.
Mathematical Reviews (MathSciNet): MR2106375
Zentralblatt MATH: 1068.53016
Digital Object Identifier: doi:10.1016/j.difgeo.2004.07.003
Aso, K., Notes on some properties of the sectional curvature of the tangent bundle, Yokohama Math. J. 29 (1981), 1–5.
Mathematical Reviews (MathSciNet): MR649233
Zentralblatt MATH: 0487.53015
Calvo, M. C. and Keilhauer, G. R., Tensor field of type (0,2) on the tangent bundle of a Riemannian manifold, Geometriae Dedicata 71 (1998), 209–219.
Mathematical Reviews (MathSciNet): MR1629795
Zentralblatt MATH: 0921.53013
Digital Object Identifier: doi:10.1023/A:1005084210109
Gudmundsson S. and Kappos E., On the geometry of the tangent bundle with the Cheeger-Gromoll metric, Tokyo J. Math. 25 (2002), 1: 75–83.
Mathematical Reviews (MathSciNet): MR1908215
Zentralblatt MATH: 1019.53017
Digital Object Identifier: doi:10.3836/tjm/1244208938
Project Euclid: euclid.tjm/1244208938
Henry, G., A new formalism for the study of natural tensors of type (0,2) on manifolds and fibrations, JP Journal of Geometry and Topology (2011), 11 2: 147–180.
Mathematical Reviews (MathSciNet): MR2895128
Zentralblatt MATH: 1231.53015
Henry, G., Tensores naturales sobre variedades y fibraciones, Doctoral Thesis. Universidad de Buenos Aires (2009) (In Spanish). http://digital.bl.fcen.uba.ar/Download/Tesis/Tesis_4540_Henry.pdf
Kowalski O., Curvature of the induced Riemannian metric on the tangent bundle of a Riemannian manifold, J. Reine Angew.Math. 250 (1971), 124–129.
Mathematical Reviews (MathSciNet): MR286028
Kowalski, O. and Sekizawa, M., Natural transformation of Riemannian metrics on manifolds to metrics on tangent bundles- a classification, Bull. Tokyo Gakugei. Univ. 4 (1988), 1–29.
Mathematical Reviews (MathSciNet): MR974641
Musso, E. and Tricerri, F., Riemannian metrics on the tangent bundles, Ann. Mat. Pura. Appl.(4), 150 (1988), 1–19.
Mathematical Reviews (MathSciNet): MR946027
Zentralblatt MATH: 0658.53045
Digital Object Identifier: doi:10.1007/BF01761461
O'Neill, B., The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459–469.
Mathematical Reviews (MathSciNet): MR200865
Digital Object Identifier: doi:10.1307/mmj/1028999604
Project Euclid: euclid.mmj/1028999604
Sekizawa, M., Curvatures of the tangent bundles with Cheeger-Gromoll metric, Tokyo J. Math. 14 (1991), 2: 407–417.
Mathematical Reviews (MathSciNet): MR1138176
Zentralblatt MATH: 0768.53020
Digital Object Identifier: doi:10.3836/tjm/1270130381
Project Euclid: euclid.tjm/1270130381
P. B. Bhattacharya, The Hilbert function of two ideals, Proc. Cambridge. Philos. Soc. 53(1957), 568-575.
Mathematical Reviews (MathSciNet): MR89835
Digital Object Identifier: doi:10.1017/S0305004100032618
previous :: next
2013 © Publication Committee for the Tokyo Journal of Mathematics
Tokyo Journal of Mathematics
