Abstract:
On the normal bundle of a submanifold in a Riemannian space a natural Riemannian metric is introduced. The structure of surfaces with strongly parabolic normal bundle metric is determined. It is shown that the Sasaki metric of the normal bundle of vectors of fixed length of a two-dimensional Veronese surface has constant sectional curvature.
Bibliography: 15 titles.
Citation:
A. A. Borisenko, A. L. Yampol'skii, “On the Sasaki metric of the normal bundle of a submanifold in a Riemannian space”, Math. USSR-Sb., 62:1 (1989), 157–175
\Bibitem{BorYam87}
\by A.~A.~Borisenko, A.~L.~Yampol'skii
\paper On the Sasaki metric of the normal bundle of a~submanifold in a~Riemannian space
\jour Math. USSR-Sb.
\yr 1989
\vol 62
\issue 1
\pages 157--175
\mathnet{http://mi.mathnet.ru/eng/sm2664}
\crossref{https://doi.org/10.1070/SM1989v062n01ABEH003233}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=922413}
\zmath{https://zbmath.org/?q=an:0663.53035|0633.53071}
Linking options:
https://www.mathnet.ru/eng/sm2664
https://doi.org/10.1070/SM1989v062n01ABEH003233
https://www.mathnet.ru/eng/sm/v176/i2/p158
This publication is cited in the following 3 articles:
Lei Sun, Zhong-Hua Hou, “Normal Bundles of Surfaces in Riemannian Manifolds”, Mediterr. J. Math, 2014
Po-Hsun Hsieh, “Symplectic Geometry of Vector Bundle Maps of Tangent Bundles”, Rocky Mountain J. Math., 31:3 (2001)
A. A. Borisenko, A. L. Yampol'skii, “Riemannian geometry of fibre bundles”, Russian Math. Surveys, 46:6 (1991), 55–106
Citation in format AMSBIB
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