Abstract
We shall consider isometric immersions \(x:{\text M}^{n}\rightarrow\,\,{\text X}^{n+1}\) of a compact, connected, orientable, n-dimensional \((n\geq 2),{\text C}^\infty\) Riemannian manifold \({\text M}^{n}\) in a simply connected Riemannian manifold \({\text X}^{n+1}\) of constant sectional curvature.
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Communicated by S. S. Chern, April 17, 1969. The first author was a Guggenheim fellow supported partially by NSF grant GP 6974 and C.N.Pq., and the second author was supported in part by NSF grants GP 6895 and GP 6974.
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Carmo, M.P.d., Warner, F.W. (2012). Rigidity and Convexity of Hypersurfaces in Spheres. In: Tenenblat, K. (eds) Manfredo P. do Carmo – Selected Papers. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25588-5_6
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DOI: https://doi.org/10.1007/978-3-642-25588-5_6
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