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Dergiler / International Electronic Journal of Geometry / 2019 / Volume: 12 Issue: 2

Convex and Starshaped Sets in Manifolds Without Conjugate Points

Sameh Shenawy
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Yayın Tarihi
2019-10-03
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Shenawy, S. (2019). Convex and Starshaped Sets in Manifolds Without Conjugate Points. International Electronic Journal of Geometry, Volume: 12 Issue: 2. https://doi.org/10.36890/iejg.628087

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Kaynakça (22)

  1. Alexander, S., Local and global convexity in complete Riemannian manifolds. Pacific Journal of Mathematics 76(1978), no. 2, 283-289.
  2. Balashov, M. V., An Analog of the Krein-Mil’man Theorem for Strongly Convex Hulls in Hilbert Space. Mathematical Notes 71(2002), no. 1-2, 34-38.
  3. Beltagy, M., Sufficient conditions for convexity in manifolds without focal points. Comment. Math. Univ. Carolinae 34 (1993), 443-449.
  4. Beltagy, M., Local and global exposed points. Acta Mathematica Scientia 15(1995), no. 3, 335-341.
  5. Beltagy, M., On starshaped sets. Bull. Malays. Math. Soc., II. Ser. 11(1988), no. 2, 49–57.
  6. Burns, K., The flat strip theorem fails for surfaces with no conjugate points. Proceedings of the American Mathematical Society 115(1992), no. 1, 199-206.
  7. Eberlein, P., Geodesic flow in certain manifolds without conjugate points. Transactions of the American Mathematical Society 167 (1972), 151-170.
  8. Emmerich, P., Rigidity of complete Riemannian manifolds without conjugate points. Shaker Verlag Gmbh, Germa, 2013.
  9. Green, L. W., Surfaces without conjugate points. Transactions of the American Mathematical Society 76(1954), no. 3, 529-546.
  10. Goto, M. S., Manifolds without focal points. Journal of Differential Geometry 13(1978), no. 3, 341-359.
  11. Gulliver, R., On the variety of manifolds without conjugate points. Transactions of the American Mathematical Society 210 (1975), 185-201.
  12. Ivanov, S. and Vitali K. Manifolds without conjugate points and their fundamental groups. Journal of Differential Geometry 96(2014), no. 2, 223-240.
  13. Jaume, D. A. and Rubén, P., Conjugacy for closed convex sets. Contributions to Algebra and Geometry 46 (2005), no. 1, 131-149.
  14. Lay, S.R., Convex sets and their applications. Courier Corporation, 2007.
  15. Li, S. and Yicheng G., On the relations of a convex set and its profile. In Integral Geometry and Convexity pp. 199-211. 2006.
  16. Alexander, S., Local and global convexity in complete Riemannian manifolds. Pacific Journal of Mathematics 76(1978), no. 2, 283-289.
  17. Balashov, M. V., An Analog of the Krein-Mil’man Theorem for Strongly Convex Hulls in Hilbert Space. Mathematical Notes 71(2002), no. 1-2, 34-38.
  18. Beltagy, M., Local and global exposed points. Acta Mathematica Scientia 15(1995), no. 3, 335-341.
  19. Beltagy, M., On starshaped sets. Bull. Malays. Math. Soc., II. Ser. 11(1988), no. 2, 49–57.
  20. Green, L. W., Surfaces without conjugate points. Transactions of the American Mathematical Society 76(1954), no. 3, 529-546.
  21. Goto, M. S., Manifolds without focal points. Journal of Differential Geometry 13(1978), no. 3, 341-359.
  22. Ivanov, S. and Vitali K. Manifolds without conjugate points and their fundamental groups. Journal of Differential Geometry 96(2014), no. 2, 223-240.