Curvatures of the diagonal lift from an affine manifold to the linear frame bundle

• Autorzy: Oldřich Kowalski , Masami Sekizawa
• Języki publikacji: EN

Abstrakty

EN

We investigate the curvature of the so-called diagonal lift from an affine manifold to the linear frame bundle LM. This is an affine analogue (but not a direct generalization) of the Sasaki-Mok metric on LM investigated by L.A. Cordero and M. de León in 1986. The Sasaki-Mok metric is constructed over a Riemannian manifold as base manifold. We receive analogous and, surprisingly, even stronger results in our affine setting.

Słowa kluczowe

EN

Riemannian manifold; Linear frame bundle; Natural metric; Affine connection; Sasaki-Mok metric

Kategorie tematyczne

• 53C20: Global Riemannian geometry, including pinching
• 53C07: Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
• 53B05: Linear and affine connections

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 837-843

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Oldřich Kowalski

• Charles University in Prague

autor

Masami Sekizawa

• Tokyo Gakugei University

Bibliografia

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• [10] Kowalski O., Sekizawa M., Invariance of the naturally lifted metrics on linear frame bundles over affine manifolds, Publ. Math. Debrecen (in press), preprint available at http://www.u-gakugei.ac.jp/~sekizawa/Invariance.pdf
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Identyfikatory

DOI

10.2478/s11533-012-0033-7