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References

  1. Alexander, S.—Locally convex hypersurfaces of negatively curved spaces. Proc. Am. Math. Soc. 64 (1977), 321–325.

    Article  MATH  Google Scholar 

  2. Bishop, R.L.—Infinitesimal convexity implies local convexity, Indiana Math. J. 29 (1974), 169–172.

    Article  MathSciNet  Google Scholar 

  3. do Carmo, M.P., and Lima, E.L.—Isometric immersions with semi-definite second quadratic forms. Archiv der Math. 20 (1969), 173–175.

    Article  MATH  Google Scholar 

  4. do Carmo, M.P. and Warner, F.—Rigidity and convexity of hypersurfaces in spheres. J. Diff. Geom. 4 (1970), 133–144.

    MATH  Google Scholar 

  5. Cheeger, J. and Ebin, D.G.—Comparison Theorems in Riemannian Geometry. North-Holand Publishing Co., Amsterdam, 1975.

    MATH  Google Scholar 

  6. Hadamard, J.—Sur certaines propriétés des trajectories en dynamique. J. Math. Pures Appl. 3 (1897), 331–387.

    Google Scholar 

  7. Im Hof, H.C. and Ruh, E.A.—An equivariant pinching theorem. Comm. Math. Helv. 50 (1975), 389–401.

    Article  MATH  MathSciNet  Google Scholar 

  8. Lima, E.L.—Commuting Vector Fields on S3. Ann. of Math. 81 (1965), 70–81.

    Article  MathSciNet  Google Scholar 

  9. Maeda, M.—On the injective radius of noncompact Riemannian Manifold. Proc. Japan Acad. 50 (1974), 148–151.

    Article  MATH  MathSciNet  Google Scholar 

  10. Nash, J.—The embedding problem for Riemannian manifolds. Ann. of Math. 63 (1956), 20–63.

    Article  MathSciNet  Google Scholar 

  11. Sacksteder, R.—On hypersurfaces with no negative sectional curvatures. Amer. J. Math. 82 (1960), 609–630.

    Article  MATH  MathSciNet  Google Scholar 

  12. Stokes, J.J.—Über die Gestalt der positiv, gekrümmten offenen Fläche. Compositio Mathematica 3 (1936), 55–88.

    MathSciNet  Google Scholar 

  13. Tribuzy, I.A.—Convexidade em Variedades Riemannianas Tese IMPA, 1978.

  14. Tribuzy, I.A.—Convexity in Riemannian Manifolds. An. Acad. Bras. Cienc. (1978), 50 (3).

    Google Scholar 

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Tribuzy, I.A. Convex immersions into positively-curved manifolds. Bol. Soc. Bras. Mat 17, 21–39 (1986). https://doi.org/10.1007/BF02585474

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  • DOI: https://doi.org/10.1007/BF02585474

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