A Metric on the Manifold of Immersions and Its Riemannian Curvature.
Gerd Kainz (1984)
Monatshefte für Mathematik
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Gerd Kainz (1984)
Monatshefte für Mathematik
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Neculai Papaghiuc (2001)
Colloquium Mathematicae
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We consider a certain pseudo-Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g) and obtain necessary and sufficient conditions for the pseudo-Riemannian manifold (TM,G) to be Ricci flat (see Theorem 2).
Labbi, M.-L. (2007)
Balkan Journal of Geometry and its Applications (BJGA)
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Luis Guijarro, Peter Petersen (1997)
Annales scientifiques de l'École Normale Supérieure
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M. T. K. Abbassi, Giovanni Calvaruso (2012)
Archivum Mathematicum
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We completely classify Riemannian -natural metrics of constant sectional curvature on the unit tangent sphere bundle of a Riemannian manifold . Since the base manifold turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian -natural metric on the unit tangent sphere bundle of a Riemannian surface.
Kowalski, O., Sekizawa, M. (2005)
Rendiconti del Seminario Matematico
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Oldřich Kowalski, Masami Sekizawa (2012)
Open Mathematics
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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.
Cho, Jong Taek (2000)
International Journal of Mathematics and Mathematical Sciences
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Mileva Prvanović (1993)
Matematički Vesnik
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Helmut Reckziegel (1981)
Journal für die reine und angewandte Mathematik
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