Normal Bundles of Surfaces in Riemannian Manifolds
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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.
Mathematics Subject Classification (2000)90C33 90C30
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