Abstract
Let f : S → M n be an immersed surface in a Riemannian manifold M. Let NS be the normal bundle of S in M and TM be the tangent bundle of M. Let F : (NS, g a,b ) → (TM, G a,b ) be the natural isometric immersion induced by f with g a,b = F * G a,b , where G a,b is the Cheeger–Gromoll type metric on TM. In this paper, we study the extrinsic geometric properties of NS in (TM, G a,b ) in terms of properties of the immersion f. In particular, the conditions of minimality and constant mean curvature are studied.
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This work was supported in part by the Fundamental Research Funds for the Central Universities.
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Sun, L., Hou, ZH. Normal Bundles of Surfaces in Riemannian Manifolds. Mediterr. J. Math. 12, 173–185 (2015). https://doi.org/10.1007/s00009-014-0390-5
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DOI: https://doi.org/10.1007/s00009-014-0390-5